module Graded.Modality.Morphism.Examples where
open import Tools.Bool
open import Tools.Empty
open import Tools.Function
open import Tools.Nat using (1+)
open import Tools.Product
open import Tools.PropositionalEquality
import Tools.Reasoning.PartialOrder
open import Tools.Relation
open import Tools.Sum using (_⊎_; inj₁; inj₂)
open import Tools.Unit
open import Graded.Modality
open import Graded.Modality.Instances.Affine as A
using (Affine; affineModality)
open import Graded.Modality.Instances.Erasure as E
using (Erasure; 𝟘; ω)
open import Graded.Modality.Instances.Erasure.Modality as E
using (ErasureModality)
import Graded.Modality.Instances.Erasure.Properties as EP
open import Graded.Modality.Instances.Linear-or-affine as LA
using (Linear-or-affine; 𝟘; 𝟙; ≤𝟙; ≤ω; linear-or-affine)
open import Graded.Modality.Instances.Linearity as L
using (Linearity; linearityModality)
open import Graded.Modality.Instances.Unit
using (UnitModality; unit-has-nr)
open import Graded.Modality.Instances.Zero-one-many as ZOM
using (Zero-one-many; 𝟘; 𝟙; ω; zero-one-many-modality)
open import Graded.Modality.Morphism
import Graded.Modality.Properties
open import Graded.Modality.Variant
open Modality-variant
private variable
𝟙≤𝟘 : Bool
v₁ v₂ : Modality-variant _
A M : Set _
v₁-ok v₂-ok : A
p q₁ q₂ q₃ q₄ r : M
unit→erasure : ⊤ → Erasure
unit→erasure _ = ω
erasure→unit : Erasure → ⊤
erasure→unit = _
erasure→zero-one-many : Erasure → Zero-one-many 𝟙≤𝟘
erasure→zero-one-many = λ where
𝟘 → 𝟘
ω → ω
erasure→zero-one-many-Σ : Erasure → Zero-one-many 𝟙≤𝟘
erasure→zero-one-many-Σ = λ where
𝟘 → 𝟘
ω → 𝟙
zero-one-many→erasure : Zero-one-many 𝟙≤𝟘 → Erasure
zero-one-many→erasure = λ where
𝟘 → 𝟘
_ → ω
linearity→linear-or-affine : Linearity → Linear-or-affine
linearity→linear-or-affine = λ where
𝟘 → 𝟘
𝟙 → 𝟙
ω → ≤ω
linear-or-affine→linearity : Linear-or-affine → Linearity
linear-or-affine→linearity = λ where
𝟘 → 𝟘
𝟙 → 𝟙
≤𝟙 → ω
≤ω → ω
affine→linear-or-affine : Affine → Linear-or-affine
affine→linear-or-affine = λ where
𝟘 → 𝟘
𝟙 → ≤𝟙
ω → ≤ω
affine→linear-or-affine-Σ : Affine → Linear-or-affine
affine→linear-or-affine-Σ = λ where
𝟘 → 𝟘
𝟙 → 𝟙
ω → ≤ω
linear-or-affine→affine : Linear-or-affine → Affine
linear-or-affine→affine = λ where
𝟘 → 𝟘
𝟙 → 𝟙
≤𝟙 → 𝟙
≤ω → ω
affine→linearity : Affine → Linearity
affine→linearity =
linear-or-affine→linearity ∘→ affine→linear-or-affine
affine→linearity-Σ : Affine → Linearity
affine→linearity-Σ =
linear-or-affine→linearity ∘→ affine→linear-or-affine-Σ
linearity→affine : Linearity → Affine
linearity→affine =
linear-or-affine→affine ∘→ linearity→linear-or-affine
unit⇨erasure :
let 𝕄₁ = UnitModality v₁ v₁-ok
𝕄₂ = ErasureModality v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ unit→erasure
unit⇨erasure {v₁-ok} = λ where
.tr-order-reflecting _ → refl
.trivial _ _ → refl
.tr-≤ → _ , refl
.tr-≤-𝟙 _ → refl
.tr-ω → refl
.tr-≤-+ _ → _ , _ , refl , refl , refl
.tr-≤-· _ → _ , refl , refl
.tr-≤-∧ _ → _ , _ , refl , refl , refl
.tr-morphism → λ where
.first-trivial-if-second-trivial
()
.𝟘ᵐ-in-second-if-in-first → ⊥-elim ∘→ v₁-ok
.tr-𝟘-≤ → refl
.trivial-⊎-tr-≡-𝟘-⇔ → inj₁ refl
.tr-<-𝟘 _ _ → refl , λ ()
.tr-𝟙 → refl
.tr-ω → refl
.tr-+ → refl
.tr-· → refl
.tr-∧ → refl
where
open Is-morphism
open Is-order-embedding
¬erasure⇨unit :
¬ Is-morphism (ErasureModality v₁) (UnitModality v₂ v₂-ok)
erasure→unit
¬erasure⇨unit m =
case Is-morphism.first-trivial-if-second-trivial m refl of λ ()
erasure⇨zero-one-many :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = ErasureModality v₁
𝕄₂ = zero-one-many-modality 𝟙≤𝟘 v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ erasure→zero-one-many
erasure⇨zero-one-many {v₁ = v₁@record{}} {v₂} {𝟙≤𝟘 = 𝟙≤𝟘} refl =
λ where
.Is-order-embedding.trivial not-ok ok → ⊥-elim (not-ok ok)
.Is-order-embedding.tr-≤ → ω , refl
.Is-order-embedding.tr-≤-𝟙 → tr-≤-𝟙 _
.Is-order-embedding.tr-ω → refl
.Is-order-embedding.tr-≤-+ → tr-≤-+ _ _ _
.Is-order-embedding.tr-≤-· → tr-≤-· _ _ _
.Is-order-embedding.tr-≤-∧ → tr-≤-∧ _ _ _
.Is-order-embedding.tr-order-reflecting →
tr-order-reflecting _ _
.Is-order-embedding.tr-morphism → λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· {p = p} → tr-· p _
.Is-morphism.tr-∧ {p = p} → ≤-reflexive (tr-∧ p _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
module 𝟘𝟙ω = ZOM 𝟙≤𝟘
module P₁ = Graded.Modality.Properties (ErasureModality v₁)
open Graded.Modality.Properties (zero-one-many-modality 𝟙≤𝟘 v₂)
open Tools.Reasoning.PartialOrder ≤-poset
tr′ = erasure→zero-one-many
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 ω ()
tr-≤-𝟙 : ∀ p → tr′ p 𝟘𝟙ω.≤ 𝟙 → p E.≤ ω
tr-≤-𝟙 𝟘 𝟘≡𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
tr-≤-𝟙 ω _ = refl
tr-+ : ∀ p q → tr′ (p E.+ q) ≡ tr′ p 𝟘𝟙ω.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p E.· q) ≡ tr′ p 𝟘𝟙ω.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 ω = refl
tr-· ω 𝟘 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p E.∧ q) ≡ tr′ p 𝟘𝟙ω.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω ω = refl
tr-order-reflecting : ∀ p q → tr′ p 𝟘𝟙ω.≤ tr′ q → p E.≤ q
tr-order-reflecting 𝟘 𝟘 _ = refl
tr-order-reflecting ω 𝟘 _ = refl
tr-order-reflecting ω ω _ = refl
tr-order-reflecting 𝟘 ω ()
tr-≤-+ :
∀ p q r →
tr′ p 𝟘𝟙ω.≤ q 𝟘𝟙ω.+ r →
∃₂ λ q′ r′ → tr′ q′ 𝟘𝟙ω.≤ q × tr′ r′ 𝟘𝟙ω.≤ r × p E.≤ q′ E.+ r′
tr-≤-+ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-+ 𝟘 𝟘 𝟙 𝟘≡𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
tr-≤-+ 𝟘 𝟙 𝟘 𝟘≡𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
tr-≤-+ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-+ 𝟘 𝟘 ω ()
tr-≤-+ 𝟘 𝟙 𝟙 ()
tr-≤-+ 𝟘 𝟙 ω ()
tr-≤-+ 𝟘 ω 𝟘 ()
tr-≤-+ 𝟘 ω 𝟙 ()
tr-≤-+ 𝟘 ω ω ()
tr-≤-· :
∀ p q r →
tr′ p 𝟘𝟙ω.≤ tr′ q 𝟘𝟙ω.· r →
∃ λ r′ → tr′ r′ 𝟘𝟙ω.≤ r × p E.≤ q E.· r′
tr-≤-· 𝟘 𝟘 _ _ = ω , refl , refl
tr-≤-· 𝟘 ω 𝟘 _ = 𝟘 , refl , refl
tr-≤-· ω _ _ _ = ω , refl , refl
tr-≤-· 𝟘 ω 𝟙 ()
tr-≤-· 𝟘 ω ω ()
tr-≤-∧ :
∀ p q r →
tr′ p 𝟘𝟙ω.≤ q 𝟘𝟙ω.∧ r →
∃₂ λ q′ r′ → tr′ q′ 𝟘𝟙ω.≤ q × tr′ r′ 𝟘𝟙ω.≤ r × p E.≤ q′ E.∧ r′
tr-≤-∧ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-∧ 𝟘 𝟘 𝟙 𝟘≤𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘≰𝟘∧𝟙 𝟘≤𝟘∧𝟙)
tr-≤-∧ 𝟘 𝟙 𝟘 𝟘≤𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘≰𝟘∧𝟙 𝟘≤𝟘∧𝟙)
tr-≤-∧ 𝟘 𝟙 𝟙 𝟘≡𝟘∧𝟙 = ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
tr-≤-∧ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-∧ 𝟘 𝟘 ω ()
tr-≤-∧ 𝟘 𝟙 ω ()
tr-≤-∧ 𝟘 ω 𝟘 ()
tr-≤-∧ 𝟘 ω 𝟙 ()
tr-≤-∧ 𝟘 ω ω ()
zero-one-many⇨erasure :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = zero-one-many-modality 𝟙≤𝟘 v₁
𝕄₂ = ErasureModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ zero-one-many→erasure
zero-one-many⇨erasure {v₂ = v₂@record{}} {𝟙≤𝟘 = 𝟙≤𝟘} refl = λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· {p = p} → tr-· p _
.Is-morphism.tr-∧ {p = p} → ≤-reflexive (tr-∧ p _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
module 𝟘𝟙ω = ZOM 𝟙≤𝟘
open Graded.Modality.Properties (ErasureModality v₂)
tr′ = zero-one-many→erasure
tr-𝟘∧𝟙 : tr′ 𝟘𝟙ω.𝟘∧𝟙 ≡ ω
tr-𝟘∧𝟙 = 𝟘𝟙ω.𝟘∧𝟙-elim
(λ p → tr′ p ≡ ω)
(λ _ → refl)
(λ _ → refl)
tr-ω[𝟘∧𝟙] : tr′ (ω 𝟘𝟙ω.· 𝟘𝟙ω.𝟘∧𝟙) ≡ ω
tr-ω[𝟘∧𝟙] = cong tr′ (𝟘𝟙ω.ω·≢𝟘 𝟘𝟙ω.𝟘∧𝟙≢𝟘)
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ω ()
tr-+ : ∀ p q → tr′ (p 𝟘𝟙ω.+ q) ≡ tr′ p E.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω 𝟙 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p 𝟘𝟙ω.· q) ≡ tr′ p E.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ω = refl
tr-· ω 𝟘 = refl
tr-· ω 𝟙 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p 𝟘𝟙ω.∧ q) ≡ tr′ p E.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = tr-𝟘∧𝟙
tr-∧ 𝟘 ω = refl
tr-∧ 𝟙 𝟘 = tr-𝟘∧𝟙
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω 𝟙 = refl
tr-∧ ω ω = refl
¬zero-one-many⇨erasure :
¬ Is-order-embedding
(zero-one-many-modality 𝟙≤𝟘 v₁)
(ErasureModality v₂)
zero-one-many→erasure
¬zero-one-many⇨erasure m =
case Is-order-embedding.tr-injective m {p = 𝟙} {q = ω} refl of λ ()
erasure⇨linearity :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = ErasureModality v₁
𝕄₂ = linearityModality v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ erasure→zero-one-many
erasure⇨linearity = erasure⇨zero-one-many
linearity⇨erasure :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = linearityModality v₁
𝕄₂ = ErasureModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ zero-one-many→erasure
linearity⇨erasure = zero-one-many⇨erasure
¬linearity⇨erasure :
¬ Is-order-embedding (linearityModality v₁) (ErasureModality v₂)
zero-one-many→erasure
¬linearity⇨erasure = ¬zero-one-many⇨erasure
erasure⇨affine :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = ErasureModality v₁
𝕄₂ = affineModality v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ erasure→zero-one-many
erasure⇨affine = erasure⇨zero-one-many
affine⇨erasure :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = affineModality v₁
𝕄₂ = ErasureModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ zero-one-many→erasure
affine⇨erasure = zero-one-many⇨erasure
¬affine⇨erasure :
¬ Is-order-embedding (affineModality v₁) (ErasureModality v₂)
zero-one-many→erasure
¬affine⇨erasure = ¬zero-one-many⇨erasure
linearity⇨linear-or-affine :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = linearityModality v₁
𝕄₂ = linear-or-affine v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ linearity→linear-or-affine
linearity⇨linear-or-affine {v₁ = v₁@record{}} {v₂} refl = λ where
.Is-order-embedding.trivial not-ok ok → ⊥-elim (not-ok ok)
.Is-order-embedding.tr-≤ → ω , refl
.Is-order-embedding.tr-≤-𝟙 → tr-≤-𝟙 _
.Is-order-embedding.tr-ω → refl
.Is-order-embedding.tr-≤-+ → tr-≤-+ _ _ _
.Is-order-embedding.tr-≤-· → tr-≤-· _ _ _
.Is-order-embedding.tr-≤-∧ → tr-≤-∧ _ _ _
.Is-order-embedding.tr-order-reflecting → tr-order-reflecting _ _
.Is-order-embedding.tr-morphism → λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ → tr-∧ _ _
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
module P₁ = Graded.Modality.Properties (linearityModality v₁)
open Graded.Modality.Properties (linear-or-affine v₂)
tr′ = linearity→linear-or-affine
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ω ()
tr-≤-𝟙 : ∀ p → tr′ p LA.≤ 𝟙 → p L.≤ 𝟙
tr-≤-𝟙 𝟙 _ = refl
tr-≤-𝟙 ω _ = refl
tr-≤-𝟙 𝟘 ()
tr-+ : ∀ p q → tr′ (p L.+ q) ≡ tr′ p LA.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω 𝟙 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p L.· q) ≡ tr′ p LA.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ω = refl
tr-· ω 𝟘 = refl
tr-· ω 𝟙 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p L.∧ q) LA.≤ tr′ p LA.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = ≤-refl
tr-∧ 𝟘 ω = refl
tr-∧ 𝟙 𝟘 = ≤-refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω 𝟙 = refl
tr-∧ ω ω = refl
tr-order-reflecting : ∀ p q → tr′ p LA.≤ tr′ q → p L.≤ q
tr-order-reflecting 𝟘 𝟘 _ = refl
tr-order-reflecting 𝟙 𝟙 _ = refl
tr-order-reflecting ω 𝟘 _ = refl
tr-order-reflecting ω 𝟙 _ = refl
tr-order-reflecting ω ω _ = refl
tr-order-reflecting 𝟘 𝟙 ()
tr-order-reflecting 𝟘 ω ()
tr-order-reflecting 𝟙 𝟘 ()
tr-order-reflecting 𝟙 ω ()
tr-≤-+ :
∀ p q r →
tr′ p LA.≤ q LA.+ r →
∃₂ λ q′ r′ → tr′ q′ LA.≤ q × tr′ r′ LA.≤ r × p L.≤ q′ L.+ r′
tr-≤-+ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-+ 𝟙 𝟘 𝟙 _ = 𝟘 , 𝟙 , refl , refl , refl
tr-≤-+ 𝟙 𝟙 𝟘 _ = 𝟙 , 𝟘 , refl , refl , refl
tr-≤-+ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-+ 𝟘 𝟘 𝟙 ()
tr-≤-+ 𝟘 𝟘 ≤𝟙 ()
tr-≤-+ 𝟘 𝟘 ≤ω ()
tr-≤-+ 𝟘 𝟙 𝟘 ()
tr-≤-+ 𝟘 𝟙 𝟙 ()
tr-≤-+ 𝟘 𝟙 ≤𝟙 ()
tr-≤-+ 𝟘 𝟙 ≤ω ()
tr-≤-+ 𝟘 ≤𝟙 𝟘 ()
tr-≤-+ 𝟘 ≤𝟙 𝟙 ()
tr-≤-+ 𝟘 ≤𝟙 ≤𝟙 ()
tr-≤-+ 𝟘 ≤𝟙 ≤ω ()
tr-≤-+ 𝟘 ≤ω 𝟘 ()
tr-≤-+ 𝟘 ≤ω 𝟙 ()
tr-≤-+ 𝟘 ≤ω ≤𝟙 ()
tr-≤-+ 𝟘 ≤ω ≤ω ()
tr-≤-+ 𝟙 𝟘 𝟘 ()
tr-≤-+ 𝟙 𝟘 ≤𝟙 ()
tr-≤-+ 𝟙 𝟘 ≤ω ()
tr-≤-+ 𝟙 𝟙 𝟙 ()
tr-≤-+ 𝟙 𝟙 ≤𝟙 ()
tr-≤-+ 𝟙 𝟙 ≤ω ()
tr-≤-+ 𝟙 ≤𝟙 𝟘 ()
tr-≤-+ 𝟙 ≤𝟙 𝟙 ()
tr-≤-+ 𝟙 ≤𝟙 ≤𝟙 ()
tr-≤-+ 𝟙 ≤𝟙 ≤ω ()
tr-≤-+ 𝟙 ≤ω 𝟘 ()
tr-≤-+ 𝟙 ≤ω 𝟙 ()
tr-≤-+ 𝟙 ≤ω ≤𝟙 ()
tr-≤-+ 𝟙 ≤ω ≤ω ()
tr-≤-· :
∀ p q r →
tr′ p LA.≤ tr′ q LA.· r →
∃ λ r′ → tr′ r′ LA.≤ r × p L.≤ q L.· r′
tr-≤-· 𝟘 𝟘 𝟘 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 𝟙 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 ≤𝟙 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 ≤ω _ = ω , refl , refl
tr-≤-· 𝟘 𝟙 𝟘 _ = 𝟘 , refl , refl
tr-≤-· 𝟘 ω 𝟘 _ = 𝟘 , refl , refl
tr-≤-· 𝟙 𝟙 𝟙 _ = 𝟙 , refl , refl
tr-≤-· ω _ _ _ = ω , refl , refl
tr-≤-· 𝟘 𝟙 𝟙 ()
tr-≤-· 𝟘 𝟙 ≤𝟙 ()
tr-≤-· 𝟘 𝟙 ≤ω ()
tr-≤-· 𝟘 ω 𝟙 ()
tr-≤-· 𝟘 ω ≤𝟙 ()
tr-≤-· 𝟘 ω ≤ω ()
tr-≤-· 𝟙 𝟘 𝟘 ()
tr-≤-· 𝟙 𝟘 𝟙 ()
tr-≤-· 𝟙 𝟘 ≤𝟙 ()
tr-≤-· 𝟙 𝟘 ≤ω ()
tr-≤-· 𝟙 𝟙 𝟘 ()
tr-≤-· 𝟙 𝟙 ≤𝟙 ()
tr-≤-· 𝟙 𝟙 ≤ω ()
tr-≤-· 𝟙 ω 𝟘 ()
tr-≤-· 𝟙 ω 𝟙 ()
tr-≤-· 𝟙 ω ≤𝟙 ()
tr-≤-· 𝟙 ω ≤ω ()
tr-≤-∧ :
∀ p q r →
tr′ p LA.≤ q LA.∧ r →
∃₂ λ q′ r′ → tr′ q′ LA.≤ q × tr′ r′ LA.≤ r × p L.≤ q′ L.∧ r′
tr-≤-∧ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-∧ 𝟙 𝟙 𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-∧ 𝟘 𝟘 𝟙 ()
tr-≤-∧ 𝟘 𝟘 ≤𝟙 ()
tr-≤-∧ 𝟘 𝟘 ≤ω ()
tr-≤-∧ 𝟘 𝟙 𝟘 ()
tr-≤-∧ 𝟘 𝟙 𝟙 ()
tr-≤-∧ 𝟘 𝟙 ≤𝟙 ()
tr-≤-∧ 𝟘 𝟙 ≤ω ()
tr-≤-∧ 𝟘 ≤𝟙 𝟘 ()
tr-≤-∧ 𝟘 ≤𝟙 𝟙 ()
tr-≤-∧ 𝟘 ≤𝟙 ≤𝟙 ()
tr-≤-∧ 𝟘 ≤𝟙 ≤ω ()
tr-≤-∧ 𝟘 ≤ω 𝟘 ()
tr-≤-∧ 𝟘 ≤ω 𝟙 ()
tr-≤-∧ 𝟘 ≤ω ≤𝟙 ()
tr-≤-∧ 𝟘 ≤ω ≤ω ()
tr-≤-∧ 𝟙 𝟘 𝟘 ()
tr-≤-∧ 𝟙 𝟘 𝟙 ()
tr-≤-∧ 𝟙 𝟘 ≤𝟙 ()
tr-≤-∧ 𝟙 𝟘 ≤ω ()
tr-≤-∧ 𝟙 𝟙 𝟘 ()
tr-≤-∧ 𝟙 𝟙 ≤𝟙 ()
tr-≤-∧ 𝟙 𝟙 ≤ω ()
tr-≤-∧ 𝟙 ≤𝟙 𝟘 ()
tr-≤-∧ 𝟙 ≤𝟙 𝟙 ()
tr-≤-∧ 𝟙 ≤𝟙 ≤𝟙 ()
tr-≤-∧ 𝟙 ≤𝟙 ≤ω ()
tr-≤-∧ 𝟙 ≤ω 𝟘 ()
tr-≤-∧ 𝟙 ≤ω 𝟙 ()
tr-≤-∧ 𝟙 ≤ω ≤𝟙 ()
tr-≤-∧ 𝟙 ≤ω ≤ω ()
linear-or-affine⇨linearity :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = linear-or-affine v₁
𝕄₂ = linearityModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ linear-or-affine→linearity
linear-or-affine⇨linearity {v₂ = v₂@record{}} refl = λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ → ≤-reflexive (tr-∧ _ _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
open Graded.Modality.Properties (linearityModality v₂)
tr′ = linear-or-affine→linearity
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ≤𝟙 ()
tr-≡-𝟘 ≤ω ()
tr-+ : ∀ p q → tr′ (p LA.+ q) ≡ tr′ p L.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ≤𝟙 = refl
tr-+ 𝟘 ≤ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ≤𝟙 = refl
tr-+ 𝟙 ≤ω = refl
tr-+ ≤𝟙 𝟘 = refl
tr-+ ≤𝟙 𝟙 = refl
tr-+ ≤𝟙 ≤𝟙 = refl
tr-+ ≤𝟙 ≤ω = refl
tr-+ ≤ω 𝟘 = refl
tr-+ ≤ω 𝟙 = refl
tr-+ ≤ω ≤𝟙 = refl
tr-+ ≤ω ≤ω = refl
tr-· : ∀ p q → tr′ (p LA.· q) ≡ tr′ p L.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ≤𝟙 = refl
tr-· 𝟘 ≤ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ≤𝟙 = refl
tr-· 𝟙 ≤ω = refl
tr-· ≤𝟙 𝟘 = refl
tr-· ≤𝟙 𝟙 = refl
tr-· ≤𝟙 ≤𝟙 = refl
tr-· ≤𝟙 ≤ω = refl
tr-· ≤ω 𝟘 = refl
tr-· ≤ω 𝟙 = refl
tr-· ≤ω ≤𝟙 = refl
tr-· ≤ω ≤ω = refl
tr-∧ : ∀ p q → tr′ (p LA.∧ q) ≡ tr′ p L.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = refl
tr-∧ 𝟘 ≤𝟙 = refl
tr-∧ 𝟘 ≤ω = refl
tr-∧ 𝟙 𝟘 = refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ≤𝟙 = refl
tr-∧ 𝟙 ≤ω = refl
tr-∧ ≤𝟙 𝟘 = refl
tr-∧ ≤𝟙 𝟙 = refl
tr-∧ ≤𝟙 ≤𝟙 = refl
tr-∧ ≤𝟙 ≤ω = refl
tr-∧ ≤ω 𝟘 = refl
tr-∧ ≤ω 𝟙 = refl
tr-∧ ≤ω ≤𝟙 = refl
tr-∧ ≤ω ≤ω = refl
¬linear-or-affine⇨linearity :
¬ Is-order-embedding (linear-or-affine v₁) (linearityModality v₂)
linear-or-affine→linearity
¬linear-or-affine⇨linearity m =
case Is-order-embedding.tr-injective m {p = ≤𝟙} {q = ≤ω} refl of λ ()
affine⇨linear-or-affine :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = affineModality v₁
𝕄₂ = linear-or-affine v₂
in
Is-order-embedding 𝕄₁ 𝕄₂ affine→linear-or-affine
affine⇨linear-or-affine {v₁ = v₁@record{}} {v₂} refl = λ where
.Is-order-embedding.trivial not-ok ok → ⊥-elim (not-ok ok)
.Is-order-embedding.tr-≤ → ω , refl
.Is-order-embedding.tr-≤-𝟙 → tr-≤-𝟙 _
.Is-order-embedding.tr-ω → refl
.Is-order-embedding.tr-≤-+ → tr-≤-+ _ _ _
.Is-order-embedding.tr-≤-· → tr-≤-· _ _ _
.Is-order-embedding.tr-≤-∧ → tr-≤-∧ _ _ _
.Is-order-embedding.tr-order-reflecting → tr-order-reflecting _ _
.Is-order-embedding.tr-morphism → λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ → ≤-reflexive (tr-∧ _ _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
module P₁ = Graded.Modality.Properties (affineModality v₁)
open Graded.Modality.Properties (linear-or-affine v₂)
tr′ = affine→linear-or-affine
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ω ()
tr-≤-𝟙 : ∀ p → tr′ p LA.≤ 𝟙 → p A.≤ 𝟙
tr-≤-𝟙 𝟙 _ = refl
tr-≤-𝟙 ω _ = refl
tr-≤-𝟙 𝟘 ()
tr-+ : ∀ p q → tr′ (p A.+ q) ≡ tr′ p LA.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω 𝟙 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p A.· q) ≡ tr′ p LA.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ω = refl
tr-· ω 𝟘 = refl
tr-· ω 𝟙 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p A.∧ q) ≡ tr′ p LA.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = refl
tr-∧ 𝟘 ω = refl
tr-∧ 𝟙 𝟘 = refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω 𝟙 = refl
tr-∧ ω ω = refl
tr-order-reflecting : ∀ p q → tr′ p LA.≤ tr′ q → p A.≤ q
tr-order-reflecting 𝟘 𝟘 _ = refl
tr-order-reflecting 𝟙 𝟘 _ = refl
tr-order-reflecting 𝟙 𝟙 _ = refl
tr-order-reflecting ω 𝟘 _ = refl
tr-order-reflecting ω 𝟙 _ = refl
tr-order-reflecting ω ω _ = refl
tr-order-reflecting 𝟘 𝟙 ()
tr-order-reflecting 𝟘 ω ()
tr-order-reflecting 𝟙 ω ()
tr-≤-+ :
∀ p q r →
tr′ p LA.≤ q LA.+ r →
∃₂ λ q′ r′ → tr′ q′ LA.≤ q × tr′ r′ LA.≤ r × p A.≤ q′ A.+ r′
tr-≤-+ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-+ 𝟙 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-+ 𝟙 𝟘 𝟙 _ = 𝟘 , 𝟙 , refl , refl , refl
tr-≤-+ 𝟙 𝟘 ≤𝟙 _ = 𝟘 , 𝟙 , refl , refl , refl
tr-≤-+ 𝟙 𝟙 𝟘 _ = 𝟙 , 𝟘 , refl , refl , refl
tr-≤-+ 𝟙 ≤𝟙 𝟘 _ = 𝟙 , 𝟘 , refl , refl , refl
tr-≤-+ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-+ 𝟘 𝟘 𝟙 ()
tr-≤-+ 𝟘 𝟘 ≤𝟙 ()
tr-≤-+ 𝟘 𝟘 ≤ω ()
tr-≤-+ 𝟘 𝟙 𝟘 ()
tr-≤-+ 𝟘 𝟙 𝟙 ()
tr-≤-+ 𝟘 𝟙 ≤𝟙 ()
tr-≤-+ 𝟘 𝟙 ≤ω ()
tr-≤-+ 𝟘 ≤𝟙 𝟘 ()
tr-≤-+ 𝟘 ≤𝟙 𝟙 ()
tr-≤-+ 𝟘 ≤𝟙 ≤𝟙 ()
tr-≤-+ 𝟘 ≤𝟙 ≤ω ()
tr-≤-+ 𝟘 ≤ω 𝟘 ()
tr-≤-+ 𝟘 ≤ω 𝟙 ()
tr-≤-+ 𝟘 ≤ω ≤𝟙 ()
tr-≤-+ 𝟘 ≤ω ≤ω ()
tr-≤-+ 𝟙 𝟘 ≤ω ()
tr-≤-+ 𝟙 𝟙 𝟙 ()
tr-≤-+ 𝟙 𝟙 ≤𝟙 ()
tr-≤-+ 𝟙 𝟙 ≤ω ()
tr-≤-+ 𝟙 ≤𝟙 𝟙 ()
tr-≤-+ 𝟙 ≤𝟙 ≤𝟙 ()
tr-≤-+ 𝟙 ≤𝟙 ≤ω ()
tr-≤-+ 𝟙 ≤ω 𝟘 ()
tr-≤-+ 𝟙 ≤ω 𝟙 ()
tr-≤-+ 𝟙 ≤ω ≤𝟙 ()
tr-≤-+ 𝟙 ≤ω ≤ω ()
tr-≤-· :
∀ p q r →
tr′ p LA.≤ tr′ q LA.· r →
∃ λ r′ → tr′ r′ LA.≤ r × p A.≤ q A.· r′
tr-≤-· 𝟘 𝟘 𝟘 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 𝟙 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 ≤𝟙 _ = ω , refl , refl
tr-≤-· 𝟘 𝟘 ≤ω _ = ω , refl , refl
tr-≤-· 𝟘 𝟙 𝟘 _ = 𝟘 , refl , refl
tr-≤-· 𝟘 ω 𝟘 _ = 𝟘 , refl , refl
tr-≤-· 𝟙 𝟘 𝟘 _ = ω , refl , refl
tr-≤-· 𝟙 𝟘 𝟙 _ = ω , refl , refl
tr-≤-· 𝟙 𝟘 ≤𝟙 _ = ω , refl , refl
tr-≤-· 𝟙 𝟘 ≤ω _ = ω , refl , refl
tr-≤-· 𝟙 𝟙 𝟘 _ = 𝟙 , refl , refl
tr-≤-· 𝟙 𝟙 𝟙 _ = 𝟙 , refl , refl
tr-≤-· 𝟙 𝟙 ≤𝟙 _ = 𝟙 , refl , refl
tr-≤-· 𝟙 ω 𝟘 _ = 𝟘 , refl , refl
tr-≤-· ω _ _ _ = ω , refl , refl
tr-≤-· 𝟘 𝟙 𝟙 ()
tr-≤-· 𝟘 𝟙 ≤𝟙 ()
tr-≤-· 𝟘 𝟙 ≤ω ()
tr-≤-· 𝟘 ω 𝟙 ()
tr-≤-· 𝟘 ω ≤𝟙 ()
tr-≤-· 𝟘 ω ≤ω ()
tr-≤-· 𝟙 𝟙 ≤ω ()
tr-≤-· 𝟙 ω 𝟙 ()
tr-≤-· 𝟙 ω ≤𝟙 ()
tr-≤-· 𝟙 ω ≤ω ()
tr-≤-∧ :
∀ p q r →
tr′ p LA.≤ q LA.∧ r →
∃₂ λ q′ r′ → tr′ q′ LA.≤ q × tr′ r′ LA.≤ r × p A.≤ q′ A.∧ r′
tr-≤-∧ 𝟘 𝟘 𝟘 _ = 𝟘 , 𝟘 , refl , refl , refl
tr-≤-∧ 𝟙 𝟘 𝟘 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 𝟘 𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 𝟘 ≤𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 𝟙 𝟘 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 𝟙 𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 𝟙 ≤𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 ≤𝟙 𝟘 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 ≤𝟙 𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ 𝟙 ≤𝟙 ≤𝟙 _ = 𝟙 , 𝟙 , refl , refl , refl
tr-≤-∧ ω _ _ _ = ω , ω , refl , refl , refl
tr-≤-∧ 𝟘 𝟘 𝟙 ()
tr-≤-∧ 𝟘 𝟘 ≤𝟙 ()
tr-≤-∧ 𝟘 𝟘 ≤ω ()
tr-≤-∧ 𝟘 𝟙 𝟘 ()
tr-≤-∧ 𝟘 𝟙 𝟙 ()
tr-≤-∧ 𝟘 𝟙 ≤𝟙 ()
tr-≤-∧ 𝟘 𝟙 ≤ω ()
tr-≤-∧ 𝟘 ≤𝟙 𝟘 ()
tr-≤-∧ 𝟘 ≤𝟙 𝟙 ()
tr-≤-∧ 𝟘 ≤𝟙 ≤𝟙 ()
tr-≤-∧ 𝟘 ≤𝟙 ≤ω ()
tr-≤-∧ 𝟘 ≤ω 𝟘 ()
tr-≤-∧ 𝟘 ≤ω 𝟙 ()
tr-≤-∧ 𝟘 ≤ω ≤𝟙 ()
tr-≤-∧ 𝟘 ≤ω ≤ω ()
tr-≤-∧ 𝟙 𝟘 ≤ω ()
tr-≤-∧ 𝟙 𝟙 ≤ω ()
tr-≤-∧ 𝟙 ≤𝟙 ≤ω ()
tr-≤-∧ 𝟙 ≤ω 𝟘 ()
tr-≤-∧ 𝟙 ≤ω 𝟙 ()
tr-≤-∧ 𝟙 ≤ω ≤𝟙 ()
tr-≤-∧ 𝟙 ≤ω ≤ω ()
linear-or-affine⇨affine :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = linear-or-affine v₁
𝕄₂ = affineModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ linear-or-affine→affine
linear-or-affine⇨affine {v₂ = v₂@record{}} refl = λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ → ≤-reflexive (tr-∧ _ _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
open Graded.Modality.Properties (affineModality v₂)
tr′ = linear-or-affine→affine
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ≤𝟙 ()
tr-≡-𝟘 ≤ω ()
tr-+ : ∀ p q → tr′ (p LA.+ q) ≡ tr′ p A.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ≤𝟙 = refl
tr-+ 𝟘 ≤ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ≤𝟙 = refl
tr-+ 𝟙 ≤ω = refl
tr-+ ≤𝟙 𝟘 = refl
tr-+ ≤𝟙 𝟙 = refl
tr-+ ≤𝟙 ≤𝟙 = refl
tr-+ ≤𝟙 ≤ω = refl
tr-+ ≤ω 𝟘 = refl
tr-+ ≤ω 𝟙 = refl
tr-+ ≤ω ≤𝟙 = refl
tr-+ ≤ω ≤ω = refl
tr-· : ∀ p q → tr′ (p LA.· q) ≡ tr′ p A.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ≤𝟙 = refl
tr-· 𝟘 ≤ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ≤𝟙 = refl
tr-· 𝟙 ≤ω = refl
tr-· ≤𝟙 𝟘 = refl
tr-· ≤𝟙 𝟙 = refl
tr-· ≤𝟙 ≤𝟙 = refl
tr-· ≤𝟙 ≤ω = refl
tr-· ≤ω 𝟘 = refl
tr-· ≤ω 𝟙 = refl
tr-· ≤ω ≤𝟙 = refl
tr-· ≤ω ≤ω = refl
tr-∧ : ∀ p q → tr′ (p LA.∧ q) ≡ tr′ p A.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = refl
tr-∧ 𝟘 ≤𝟙 = refl
tr-∧ 𝟘 ≤ω = refl
tr-∧ 𝟙 𝟘 = refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ≤𝟙 = refl
tr-∧ 𝟙 ≤ω = refl
tr-∧ ≤𝟙 𝟘 = refl
tr-∧ ≤𝟙 𝟙 = refl
tr-∧ ≤𝟙 ≤𝟙 = refl
tr-∧ ≤𝟙 ≤ω = refl
tr-∧ ≤ω 𝟘 = refl
tr-∧ ≤ω 𝟙 = refl
tr-∧ ≤ω ≤𝟙 = refl
tr-∧ ≤ω ≤ω = refl
¬linear-or-affine⇨affine :
¬ Is-order-embedding (linear-or-affine v₁) (affineModality v₂)
linear-or-affine→affine
¬linear-or-affine⇨affine m =
case Is-order-embedding.tr-injective m {p = 𝟙} {q = ≤𝟙} refl of λ ()
affine⇨linearity :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = affineModality v₁
𝕄₂ = linearityModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ affine→linearity
affine⇨linearity {v₁ = v₁@record{}} {v₂} refl = λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ {p = p} → ≤-reflexive (tr-∧ p _)
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
open Graded.Modality.Properties (linearityModality v₂)
tr′ = affine→linearity
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ω ()
tr-+ : ∀ p q → tr′ (p A.+ q) ≡ tr′ p L.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω 𝟙 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p A.· q) ≡ tr′ p L.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ω = refl
tr-· ω 𝟘 = refl
tr-· ω 𝟙 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p A.∧ q) ≡ tr′ p L.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = refl
tr-∧ 𝟘 ω = refl
tr-∧ 𝟙 𝟘 = refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω 𝟙 = refl
tr-∧ ω ω = refl
¬affine⇨linearity :
¬ Is-order-embedding (affineModality v₁) (linearityModality v₂)
affine→linearity
¬affine⇨linearity m =
case Is-order-embedding.tr-injective m {p = 𝟙} {q = ω} refl of λ ()
linearity⇨affine :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
let 𝕄₁ = linearityModality v₁
𝕄₂ = affineModality v₂
in
Is-morphism 𝕄₁ 𝕄₂ linearity→affine
linearity⇨affine {v₁ = v₁@record{}} {v₂} refl = λ where
.Is-morphism.first-trivial-if-second-trivial
()
.Is-morphism.tr-𝟘-≤ → refl
.Is-morphism.trivial-⊎-tr-≡-𝟘-⇔ → inj₂ ( tr-≡-𝟘 _
, λ { refl → refl }
)
.Is-morphism.tr-<-𝟘 not-ok ok → ⊥-elim (not-ok ok)
.Is-morphism.tr-𝟙 → refl
.Is-morphism.tr-ω → refl
.Is-morphism.tr-+ {p = p} → tr-+ p _
.Is-morphism.tr-· → tr-· _ _
.Is-morphism.tr-∧ {p = p} → tr-∧ p _
.Is-morphism.𝟘ᵐ-in-second-if-in-first → idᶠ
where
open Graded.Modality.Properties (affineModality v₂)
tr′ = linearity→affine
tr-≡-𝟘 : ∀ p → tr′ p ≡ 𝟘 → p ≡ 𝟘
tr-≡-𝟘 𝟘 _ = refl
tr-≡-𝟘 𝟙 ()
tr-≡-𝟘 ω ()
tr-+ : ∀ p q → tr′ (p L.+ q) ≡ tr′ p A.+ tr′ q
tr-+ 𝟘 𝟘 = refl
tr-+ 𝟘 𝟙 = refl
tr-+ 𝟘 ω = refl
tr-+ 𝟙 𝟘 = refl
tr-+ 𝟙 𝟙 = refl
tr-+ 𝟙 ω = refl
tr-+ ω 𝟘 = refl
tr-+ ω 𝟙 = refl
tr-+ ω ω = refl
tr-· : ∀ p q → tr′ (p L.· q) ≡ tr′ p A.· tr′ q
tr-· 𝟘 𝟘 = refl
tr-· 𝟘 𝟙 = refl
tr-· 𝟘 ω = refl
tr-· 𝟙 𝟘 = refl
tr-· 𝟙 𝟙 = refl
tr-· 𝟙 ω = refl
tr-· ω 𝟘 = refl
tr-· ω 𝟙 = refl
tr-· ω ω = refl
tr-∧ : ∀ p q → tr′ (p L.∧ q) A.≤ tr′ p A.∧ tr′ q
tr-∧ 𝟘 𝟘 = refl
tr-∧ 𝟘 𝟙 = ≤-refl
tr-∧ 𝟘 ω = refl
tr-∧ 𝟙 𝟘 = ≤-refl
tr-∧ 𝟙 𝟙 = refl
tr-∧ 𝟙 ω = refl
tr-∧ ω 𝟘 = refl
tr-∧ ω 𝟙 = refl
tr-∧ ω ω = refl
¬linearity⇨affine :
¬ Is-order-embedding (linearityModality v₁) (affineModality v₂)
linearity→affine
¬linearity⇨affine m =
case Is-order-embedding.tr-order-reflecting m {p = 𝟙} {q = 𝟘} refl of
λ ()
erasure⇨zero-one-many-Σ :
(T (𝟘ᵐ-allowed v₂) → T (𝟘ᵐ-allowed v₁)) →
Is-Σ-order-embedding
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
erasure→zero-one-many
erasure→zero-one-many-Σ
erasure⇨zero-one-many-Σ {𝟙≤𝟘 = 𝟙≤𝟘} ok₂₁ = record
{ tr-Σ-morphism = record
{ tr-≤-tr-Σ = λ where
{p = 𝟘} → refl
{p = ω} → refl
; tr-Σ-𝟘-≡ =
λ _ → refl
; tr-Σ-≡-𝟘-→ = λ where
{p = 𝟘} ok₂ _ → ok₂₁ ok₂ , refl
{p = ω} _ ()
; tr-Σ-≤-𝟙 = λ where
{p = ω} _ → refl
{p = 𝟘} ()
; tr-·-tr-Σ-≤ = λ where
{p = 𝟘} {q = _} → refl
{p = ω} {q = 𝟘} → refl
{p = ω} {q = ω} → refl
}
; tr-≤-tr-Σ-→ = λ where
{p = 𝟘} {q = 𝟘} _ → ω , refl , refl
{p = 𝟘} {q = ω} {r = 𝟘} _ → 𝟘 , refl , refl
{p = 𝟘} {q = ω} {r = 𝟙} 𝟘≡𝟘∧𝟙 → ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
{p = 𝟘} {q = ω} {r = ω} ()
{p = ω} _ → ω , refl , refl
}
where
module 𝟘𝟙ω = ZOM 𝟙≤𝟘
erasure⇨linearity-Σ :
(T (𝟘ᵐ-allowed v₂) → T (𝟘ᵐ-allowed v₁)) →
Is-Σ-order-embedding (ErasureModality v₁) (linearityModality v₂)
erasure→zero-one-many erasure→zero-one-many-Σ
erasure⇨linearity-Σ = erasure⇨zero-one-many-Σ
erasure⇨linearity-Σ-not-monotone :
¬ (∀ {p q} →
p E.≤ q →
erasure→zero-one-many-Σ p L.≤ erasure→zero-one-many-Σ q)
erasure⇨linearity-Σ-not-monotone mono =
case mono {p = ω} {q = 𝟘} refl of λ ()
erasure⇨affine-Σ :
(T (𝟘ᵐ-allowed v₂) → T (𝟘ᵐ-allowed v₁)) →
Is-Σ-order-embedding (ErasureModality v₁) (affineModality v₂)
erasure→zero-one-many erasure→zero-one-many-Σ
erasure⇨affine-Σ = erasure⇨zero-one-many-Σ
affine⇨linear-or-affine-Σ :
(T (𝟘ᵐ-allowed v₂) → T (𝟘ᵐ-allowed v₁)) →
Is-Σ-order-embedding (affineModality v₁) (linear-or-affine v₂)
affine→linear-or-affine affine→linear-or-affine-Σ
affine⇨linear-or-affine-Σ ok₂₁ = record
{ tr-Σ-morphism = record
{ tr-≤-tr-Σ = λ where
{p = 𝟘} → refl
{p = 𝟙} → refl
{p = ω} → refl
; tr-Σ-𝟘-≡ =
λ _ → refl
; tr-Σ-≡-𝟘-→ = λ where
{p = 𝟘} ok₂ _ → ok₂₁ ok₂ , refl
{p = 𝟙} _ ()
{p = ω} _ ()
; tr-Σ-≤-𝟙 = λ where
{p = 𝟙} _ → refl
{p = ω} _ → refl
{p = 𝟘} ()
; tr-·-tr-Σ-≤ = λ where
{p = 𝟘} {q = _} → refl
{p = 𝟙} {q = 𝟘} → refl
{p = 𝟙} {q = 𝟙} → refl
{p = 𝟙} {q = ω} → refl
{p = ω} {q = 𝟘} → refl
{p = ω} {q = 𝟙} → refl
{p = ω} {q = ω} → refl
}
; tr-≤-tr-Σ-→ = λ where
{p = 𝟘} {q = 𝟘} _ → ω , refl , refl
{p = 𝟘} {q = 𝟙} {r = 𝟘} _ → 𝟘 , refl , refl
{p = 𝟘} {q = ω} {r = 𝟘} _ → 𝟘 , refl , refl
{p = 𝟙} {q = 𝟘} _ → ω , refl , refl
{p = 𝟙} {q = 𝟙} {r = 𝟘} _ → 𝟙 , refl , refl
{p = 𝟙} {q = 𝟙} {r = 𝟙} _ → 𝟙 , refl , refl
{p = 𝟙} {q = 𝟙} {r = ≤𝟙} _ → 𝟙 , refl , refl
{p = 𝟙} {q = ω} {r = 𝟘} _ → 𝟘 , refl , refl
{p = ω} _ → ω , refl , refl
{p = 𝟘} {q = 𝟙} {r = 𝟙} ()
{p = 𝟘} {q = 𝟙} {r = ≤𝟙} ()
{p = 𝟘} {q = 𝟙} {r = ≤ω} ()
{p = 𝟘} {q = ω} {r = 𝟙} ()
{p = 𝟘} {q = ω} {r = ≤𝟙} ()
{p = 𝟘} {q = ω} {r = ≤ω} ()
{p = 𝟙} {q = 𝟙} {r = ≤ω} ()
{p = 𝟙} {q = ω} {r = 𝟙} ()
{p = 𝟙} {q = ω} {r = ≤𝟙} ()
{p = 𝟙} {q = ω} {r = ≤ω} ()
}
affine→linear-or-affine-Σ-not-monotone :
¬ (∀ {p q} →
p A.≤ q →
affine→linear-or-affine-Σ p LA.≤ affine→linear-or-affine-Σ q)
affine→linear-or-affine-Σ-not-monotone mono =
case mono {p = 𝟙} {q = 𝟘} refl of λ ()
Σ-order-embedding-but-not-order-embedding :
∃₂ λ (M₁ M₂ : Set) →
∃₂ λ (𝕄₁ : Modality M₁) (𝕄₂ : Modality M₂) →
∃₂ λ (tr tr-Σ : M₁ → M₂) →
Is-order-embedding 𝕄₁ 𝕄₂ tr ×
Is-Σ-morphism 𝕄₁ 𝕄₂ tr tr-Σ ×
Is-Σ-order-embedding 𝕄₁ 𝕄₂ tr tr-Σ ×
¬ Is-morphism 𝕄₁ 𝕄₂ tr-Σ ×
¬ Is-order-embedding 𝕄₁ 𝕄₂ tr-Σ
Σ-order-embedding-but-not-order-embedding =
Affine , Linear-or-affine
, affineModality variant
, linear-or-affine variant
, affine→linear-or-affine , affine→linear-or-affine-Σ
, affine⇨linear-or-affine refl
, Is-Σ-order-embedding.tr-Σ-morphism (affine⇨linear-or-affine-Σ _)
, affine⇨linear-or-affine-Σ _
, affine→linear-or-affine-Σ-not-monotone ∘→ Is-morphism.tr-monotone
, affine→linear-or-affine-Σ-not-monotone ∘→
Is-order-embedding.tr-monotone
where
variant = 𝟘ᵐ-allowed-if _ true
affine⇨linearity-Σ :
(T (𝟘ᵐ-allowed v₂) → T (𝟘ᵐ-allowed v₁)) →
Is-Σ-morphism (affineModality v₁) (linearityModality v₂)
affine→linearity affine→linearity-Σ
affine⇨linearity-Σ ok₂₁ = record
{ tr-≤-tr-Σ = λ where
{p = 𝟘} → refl
{p = 𝟙} → refl
{p = ω} → refl
; tr-Σ-𝟘-≡ =
λ _ → refl
; tr-Σ-≡-𝟘-→ = λ where
{p = 𝟘} ok₂ _ → ok₂₁ ok₂ , refl
{p = 𝟙} _ ()
{p = ω} _ ()
; tr-Σ-≤-𝟙 = λ where
{p = 𝟙} _ → refl
{p = ω} _ → refl
{p = 𝟘} ()
; tr-·-tr-Σ-≤ = λ where
{p = 𝟘} {q = _} → refl
{p = 𝟙} {q = 𝟘} → refl
{p = 𝟙} {q = 𝟙} → refl
{p = 𝟙} {q = ω} → refl
{p = ω} {q = 𝟘} → refl
{p = ω} {q = 𝟙} → refl
{p = ω} {q = ω} → refl
}
affine→linearity-Σ-not-monotone :
¬ (∀ {p q} →
p A.≤ q →
affine→linearity-Σ p L.≤ affine→linearity-Σ q)
affine→linearity-Σ-not-monotone mono =
case mono {p = 𝟙} {q = 𝟘} refl of λ ()
¬affine⇨linearity-Σ :
¬ Is-Σ-order-embedding
(affineModality v₁)
(linearityModality v₂)
affine→linearity affine→linearity-Σ
¬affine⇨linearity-Σ m =
case
Is-Σ-order-embedding.tr-≤-tr-Σ-→ m {p = 𝟙} {q = ω} {r = ω} refl
of λ where
(𝟘 , () , _)
(𝟙 , _ , ())
(ω , _ , ())
opaque
unit⇒erasure-nr-preserving :
Is-nr-preserving-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
⦃ unit-has-nr ⦄
unit→erasure
unit⇒erasure-nr-preserving = λ where
.tr-nr → refl
where
open Is-nr-preserving-morphism
opaque
unit⇒erasure-no-nr-preserving :
Is-no-nr-preserving-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
unit→erasure
unit⇒erasure-no-nr-preserving = λ where
.𝟘ᵐ-in-first-if-in-second _ → inj₂ refl
.𝟘-well-behaved-in-first-if-in-second _ → inj₂ refl
where
open Is-no-nr-preserving-morphism
opaque
unit⇒erasure-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
unit→erasure
unit⇒erasure-no-nr-glb-preserving {v₂} = λ where
.tr-nrᵢ-GLB _ →
_ , GLB-const (λ { 0 → refl ; (1+ i) → refl})
.tr-nrᵢ-𝟙-GLB _ →
_ , GLB-const (λ { 0 → refl ; (1+ i) → refl})
where
open Is-no-nr-glb-preserving-morphism
open Graded.Modality.Properties (ErasureModality v₂)
opaque
erasure⇨zero-one-many-nr-preserving :
Is-nr-preserving-morphism
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
⦃ has-nr₂ = ZOM.zero-one-many-has-nr 𝟙≤𝟘 ⦄
erasure→zero-one-many
erasure⇨zero-one-many-nr-preserving {𝟙≤𝟘} {v₂} = λ where
.tr-nr {r} {z} → ≤-reflexive (tr-nr′ 𝟙≤𝟘 _ r z _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (zero-one-many-modality 𝟙≤𝟘 v₂)
tr-nr′ :
∀ 𝟙≤𝟘 →
let module 𝟘𝟙ω′ = ZOM 𝟙≤𝟘
tr = erasure→zero-one-many in
∀ p r z s n →
tr (E.nr p r z s n) ≡
𝟘𝟙ω′.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
false 𝟘 𝟘 𝟘 𝟘 𝟘 → refl
false 𝟘 𝟘 𝟘 𝟘 ω → refl
false 𝟘 𝟘 𝟘 ω 𝟘 → refl
false 𝟘 𝟘 𝟘 ω ω → refl
false 𝟘 𝟘 ω 𝟘 𝟘 → refl
false 𝟘 𝟘 ω 𝟘 ω → refl
false 𝟘 𝟘 ω ω 𝟘 → refl
false 𝟘 𝟘 ω ω ω → refl
false 𝟘 ω 𝟘 𝟘 𝟘 → refl
false 𝟘 ω 𝟘 𝟘 ω → refl
false 𝟘 ω 𝟘 ω 𝟘 → refl
false 𝟘 ω 𝟘 ω ω → refl
false 𝟘 ω ω 𝟘 𝟘 → refl
false 𝟘 ω ω 𝟘 ω → refl
false 𝟘 ω ω ω 𝟘 → refl
false 𝟘 ω ω ω ω → refl
false ω 𝟘 𝟘 𝟘 𝟘 → refl
false ω 𝟘 𝟘 𝟘 ω → refl
false ω 𝟘 𝟘 ω 𝟘 → refl
false ω 𝟘 𝟘 ω ω → refl
false ω 𝟘 ω 𝟘 𝟘 → refl
false ω 𝟘 ω 𝟘 ω → refl
false ω 𝟘 ω ω 𝟘 → refl
false ω 𝟘 ω ω ω → refl
false ω ω 𝟘 𝟘 𝟘 → refl
false ω ω 𝟘 𝟘 ω → refl
false ω ω 𝟘 ω 𝟘 → refl
false ω ω 𝟘 ω ω → refl
false ω ω ω 𝟘 𝟘 → refl
false ω ω ω 𝟘 ω → refl
false ω ω ω ω 𝟘 → refl
false ω ω ω ω ω → refl
true 𝟘 𝟘 𝟘 𝟘 𝟘 → refl
true 𝟘 𝟘 𝟘 𝟘 ω → refl
true 𝟘 𝟘 𝟘 ω 𝟘 → refl
true 𝟘 𝟘 𝟘 ω ω → refl
true 𝟘 𝟘 ω 𝟘 𝟘 → refl
true 𝟘 𝟘 ω 𝟘 ω → refl
true 𝟘 𝟘 ω ω 𝟘 → refl
true 𝟘 𝟘 ω ω ω → refl
true 𝟘 ω 𝟘 𝟘 𝟘 → refl
true 𝟘 ω 𝟘 𝟘 ω → refl
true 𝟘 ω 𝟘 ω 𝟘 → refl
true 𝟘 ω 𝟘 ω ω → refl
true 𝟘 ω ω 𝟘 𝟘 → refl
true 𝟘 ω ω 𝟘 ω → refl
true 𝟘 ω ω ω 𝟘 → refl
true 𝟘 ω ω ω ω → refl
true ω 𝟘 𝟘 𝟘 𝟘 → refl
true ω 𝟘 𝟘 𝟘 ω → refl
true ω 𝟘 𝟘 ω 𝟘 → refl
true ω 𝟘 𝟘 ω ω → refl
true ω 𝟘 ω 𝟘 𝟘 → refl
true ω 𝟘 ω 𝟘 ω → refl
true ω 𝟘 ω ω 𝟘 → refl
true ω 𝟘 ω ω ω → refl
true ω ω 𝟘 𝟘 𝟘 → refl
true ω ω 𝟘 𝟘 ω → refl
true ω ω 𝟘 ω 𝟘 → refl
true ω ω 𝟘 ω ω → refl
true ω ω ω 𝟘 𝟘 → refl
true ω ω ω 𝟘 ω → refl
true ω ω ω ω 𝟘 → refl
true ω ω ω ω ω → refl
opaque
erasure⇨zero-one-many-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
erasure→zero-one-many
erasure⇨zero-one-many-no-nr-preserving {v₁ = record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second ok → inj₁ ok
.𝟘-well-behaved-in-first-if-in-second ok →
inj₁ E.erasure-has-well-behaved-zero
where
open Is-no-nr-preserving-morphism
opaque
erasure⇨zero-one-many-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
erasure→zero-one-many
erasure⇨zero-one-many-no-nr-glb-preserving {𝟙≤𝟘} = λ where
.tr-nrᵢ-GLB p-glb → _ , ZOM.nr-nrᵢ-GLB 𝟙≤𝟘 _
.tr-nrᵢ-𝟙-GLB _ → _ , ZOM.nr-nrᵢ-GLB 𝟙≤𝟘 _
where
open Is-no-nr-glb-preserving-morphism
opaque
zero-one-many⇒erasure-nr-preserving :
Is-nr-preserving-morphism
(zero-one-many-modality 𝟙≤𝟘 v₁)
(ErasureModality v₂)
⦃ ZOM.zero-one-many-has-nr 𝟙≤𝟘 ⦄
⦃ E.erasure-has-nr ⦄
zero-one-many→erasure
zero-one-many⇒erasure-nr-preserving {𝟙≤𝟘} {v₂} = λ where
.tr-nr {r} → ≤-reflexive (tr-nr′ 𝟙≤𝟘 _ r _ _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (ErasureModality v₂)
tr-nr′ :
∀ 𝟙≤𝟘 →
let module 𝟘𝟙ω′ = ZOM 𝟙≤𝟘
tr = zero-one-many→erasure
in
∀ p r z s n →
tr (𝟘𝟙ω′.nr p r z s n) ≡
E.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
false 𝟘 𝟘 𝟘 𝟘 𝟘 → refl
false 𝟘 𝟘 𝟘 𝟘 𝟙 → refl
false 𝟘 𝟘 𝟘 𝟘 ω → refl
false 𝟘 𝟘 𝟘 𝟙 𝟘 → refl
false 𝟘 𝟘 𝟘 𝟙 𝟙 → refl
false 𝟘 𝟘 𝟘 𝟙 ω → refl
false 𝟘 𝟘 𝟘 ω 𝟘 → refl
false 𝟘 𝟘 𝟘 ω 𝟙 → refl
false 𝟘 𝟘 𝟘 ω ω → refl
false 𝟘 𝟘 𝟙 𝟘 𝟘 → refl
false 𝟘 𝟘 𝟙 𝟘 𝟙 → refl
false 𝟘 𝟘 𝟙 𝟘 ω → refl
false 𝟘 𝟘 𝟙 𝟙 𝟘 → refl
false 𝟘 𝟘 𝟙 𝟙 𝟙 → refl
false 𝟘 𝟘 𝟙 𝟙 ω → refl
false 𝟘 𝟘 𝟙 ω 𝟘 → refl
false 𝟘 𝟘 𝟙 ω 𝟙 → refl
false 𝟘 𝟘 𝟙 ω ω → refl
false 𝟘 𝟘 ω 𝟘 𝟘 → refl
false 𝟘 𝟘 ω 𝟘 𝟙 → refl
false 𝟘 𝟘 ω 𝟘 ω → refl
false 𝟘 𝟘 ω 𝟙 𝟘 → refl
false 𝟘 𝟘 ω 𝟙 𝟙 → refl
false 𝟘 𝟘 ω 𝟙 ω → refl
false 𝟘 𝟘 ω ω 𝟘 → refl
false 𝟘 𝟘 ω ω 𝟙 → refl
false 𝟘 𝟘 ω ω ω → refl
false 𝟘 𝟙 𝟘 𝟘 𝟘 → refl
false 𝟘 𝟙 𝟘 𝟘 𝟙 → refl
false 𝟘 𝟙 𝟘 𝟘 ω → refl
false 𝟘 𝟙 𝟘 𝟙 𝟘 → refl
false 𝟘 𝟙 𝟘 𝟙 𝟙 → refl
false 𝟘 𝟙 𝟘 𝟙 ω → refl
false 𝟘 𝟙 𝟘 ω 𝟘 → refl
false 𝟘 𝟙 𝟘 ω 𝟙 → refl
false 𝟘 𝟙 𝟘 ω ω → refl
false 𝟘 𝟙 𝟙 𝟘 𝟘 → refl
false 𝟘 𝟙 𝟙 𝟘 𝟙 → refl
false 𝟘 𝟙 𝟙 𝟘 ω → refl
false 𝟘 𝟙 𝟙 𝟙 𝟘 → refl
false 𝟘 𝟙 𝟙 𝟙 𝟙 → refl
false 𝟘 𝟙 𝟙 𝟙 ω → refl
false 𝟘 𝟙 𝟙 ω 𝟘 → refl
false 𝟘 𝟙 𝟙 ω 𝟙 → refl
false 𝟘 𝟙 𝟙 ω ω → refl
false 𝟘 𝟙 ω 𝟘 𝟘 → refl
false 𝟘 𝟙 ω 𝟘 𝟙 → refl
false 𝟘 𝟙 ω 𝟘 ω → refl
false 𝟘 𝟙 ω 𝟙 𝟘 → refl
false 𝟘 𝟙 ω 𝟙 𝟙 → refl
false 𝟘 𝟙 ω 𝟙 ω → refl
false 𝟘 𝟙 ω ω 𝟘 → refl
false 𝟘 𝟙 ω ω 𝟙 → refl
false 𝟘 𝟙 ω ω ω → refl
false 𝟘 ω 𝟘 𝟘 𝟘 → refl
false 𝟘 ω 𝟘 𝟘 𝟙 → refl
false 𝟘 ω 𝟘 𝟘 ω → refl
false 𝟘 ω 𝟘 𝟙 𝟘 → refl
false 𝟘 ω 𝟘 𝟙 𝟙 → refl
false 𝟘 ω 𝟘 𝟙 ω → refl
false 𝟘 ω 𝟘 ω 𝟘 → refl
false 𝟘 ω 𝟘 ω 𝟙 → refl
false 𝟘 ω 𝟘 ω ω → refl
false 𝟘 ω 𝟙 𝟘 𝟘 → refl
false 𝟘 ω 𝟙 𝟘 𝟙 → refl
false 𝟘 ω 𝟙 𝟘 ω → refl
false 𝟘 ω 𝟙 𝟙 𝟘 → refl
false 𝟘 ω 𝟙 𝟙 𝟙 → refl
false 𝟘 ω 𝟙 𝟙 ω → refl
false 𝟘 ω 𝟙 ω 𝟘 → refl
false 𝟘 ω 𝟙 ω 𝟙 → refl
false 𝟘 ω 𝟙 ω ω → refl
false 𝟘 ω ω 𝟘 𝟘 → refl
false 𝟘 ω ω 𝟘 𝟙 → refl
false 𝟘 ω ω 𝟘 ω → refl
false 𝟘 ω ω 𝟙 𝟘 → refl
false 𝟘 ω ω 𝟙 𝟙 → refl
false 𝟘 ω ω 𝟙 ω → refl
false 𝟘 ω ω ω 𝟘 → refl
false 𝟘 ω ω ω 𝟙 → refl
false 𝟘 ω ω ω ω → refl
false 𝟙 𝟘 𝟘 𝟘 𝟘 → refl
false 𝟙 𝟘 𝟘 𝟘 𝟙 → refl
false 𝟙 𝟘 𝟘 𝟘 ω → refl
false 𝟙 𝟘 𝟘 𝟙 𝟘 → refl
false 𝟙 𝟘 𝟘 𝟙 𝟙 → refl
false 𝟙 𝟘 𝟘 𝟙 ω → refl
false 𝟙 𝟘 𝟘 ω 𝟘 → refl
false 𝟙 𝟘 𝟘 ω 𝟙 → refl
false 𝟙 𝟘 𝟘 ω ω → refl
false 𝟙 𝟘 𝟙 𝟘 𝟘 → refl
false 𝟙 𝟘 𝟙 𝟘 𝟙 → refl
false 𝟙 𝟘 𝟙 𝟘 ω → refl
false 𝟙 𝟘 𝟙 𝟙 𝟘 → refl
false 𝟙 𝟘 𝟙 𝟙 𝟙 → refl
false 𝟙 𝟘 𝟙 𝟙 ω → refl
false 𝟙 𝟘 𝟙 ω 𝟘 → refl
false 𝟙 𝟘 𝟙 ω 𝟙 → refl
false 𝟙 𝟘 𝟙 ω ω → refl
false 𝟙 𝟘 ω 𝟘 𝟘 → refl
false 𝟙 𝟘 ω 𝟘 𝟙 → refl
false 𝟙 𝟘 ω 𝟘 ω → refl
false 𝟙 𝟘 ω 𝟙 𝟘 → refl
false 𝟙 𝟘 ω 𝟙 𝟙 → refl
false 𝟙 𝟘 ω 𝟙 ω → refl
false 𝟙 𝟘 ω ω 𝟘 → refl
false 𝟙 𝟘 ω ω 𝟙 → refl
false 𝟙 𝟘 ω ω ω → refl
false 𝟙 𝟙 𝟘 𝟘 𝟘 → refl
false 𝟙 𝟙 𝟘 𝟘 𝟙 → refl
false 𝟙 𝟙 𝟘 𝟘 ω → refl
false 𝟙 𝟙 𝟘 𝟙 𝟘 → refl
false 𝟙 𝟙 𝟘 𝟙 𝟙 → refl
false 𝟙 𝟙 𝟘 𝟙 ω → refl
false 𝟙 𝟙 𝟘 ω 𝟘 → refl
false 𝟙 𝟙 𝟘 ω 𝟙 → refl
false 𝟙 𝟙 𝟘 ω ω → refl
false 𝟙 𝟙 𝟙 𝟘 𝟘 → refl
false 𝟙 𝟙 𝟙 𝟘 𝟙 → refl
false 𝟙 𝟙 𝟙 𝟘 ω → refl
false 𝟙 𝟙 𝟙 𝟙 𝟘 → refl
false 𝟙 𝟙 𝟙 𝟙 𝟙 → refl
false 𝟙 𝟙 𝟙 𝟙 ω → refl
false 𝟙 𝟙 𝟙 ω 𝟘 → refl
false 𝟙 𝟙 𝟙 ω 𝟙 → refl
false 𝟙 𝟙 𝟙 ω ω → refl
false 𝟙 𝟙 ω 𝟘 𝟘 → refl
false 𝟙 𝟙 ω 𝟘 𝟙 → refl
false 𝟙 𝟙 ω 𝟘 ω → refl
false 𝟙 𝟙 ω 𝟙 𝟘 → refl
false 𝟙 𝟙 ω 𝟙 𝟙 → refl
false 𝟙 𝟙 ω 𝟙 ω → refl
false 𝟙 𝟙 ω ω 𝟘 → refl
false 𝟙 𝟙 ω ω 𝟙 → refl
false 𝟙 𝟙 ω ω ω → refl
false 𝟙 ω 𝟘 𝟘 𝟘 → refl
false 𝟙 ω 𝟘 𝟘 𝟙 → refl
false 𝟙 ω 𝟘 𝟘 ω → refl
false 𝟙 ω 𝟘 𝟙 𝟘 → refl
false 𝟙 ω 𝟘 𝟙 𝟙 → refl
false 𝟙 ω 𝟘 𝟙 ω → refl
false 𝟙 ω 𝟘 ω 𝟘 → refl
false 𝟙 ω 𝟘 ω 𝟙 → refl
false 𝟙 ω 𝟘 ω ω → refl
false 𝟙 ω 𝟙 𝟘 𝟘 → refl
false 𝟙 ω 𝟙 𝟘 𝟙 → refl
false 𝟙 ω 𝟙 𝟘 ω → refl
false 𝟙 ω 𝟙 𝟙 𝟘 → refl
false 𝟙 ω 𝟙 𝟙 𝟙 → refl
false 𝟙 ω 𝟙 𝟙 ω → refl
false 𝟙 ω 𝟙 ω 𝟘 → refl
false 𝟙 ω 𝟙 ω 𝟙 → refl
false 𝟙 ω 𝟙 ω ω → refl
false 𝟙 ω ω 𝟘 𝟘 → refl
false 𝟙 ω ω 𝟘 𝟙 → refl
false 𝟙 ω ω 𝟘 ω → refl
false 𝟙 ω ω 𝟙 𝟘 → refl
false 𝟙 ω ω 𝟙 𝟙 → refl
false 𝟙 ω ω 𝟙 ω → refl
false 𝟙 ω ω ω 𝟘 → refl
false 𝟙 ω ω ω 𝟙 → refl
false 𝟙 ω ω ω ω → refl
false ω 𝟘 𝟘 𝟘 𝟘 → refl
false ω 𝟘 𝟘 𝟘 𝟙 → refl
false ω 𝟘 𝟘 𝟘 ω → refl
false ω 𝟘 𝟘 𝟙 𝟘 → refl
false ω 𝟘 𝟘 𝟙 𝟙 → refl
false ω 𝟘 𝟘 𝟙 ω → refl
false ω 𝟘 𝟘 ω 𝟘 → refl
false ω 𝟘 𝟘 ω 𝟙 → refl
false ω 𝟘 𝟘 ω ω → refl
false ω 𝟘 𝟙 𝟘 𝟘 → refl
false ω 𝟘 𝟙 𝟘 𝟙 → refl
false ω 𝟘 𝟙 𝟘 ω → refl
false ω 𝟘 𝟙 𝟙 𝟘 → refl
false ω 𝟘 𝟙 𝟙 𝟙 → refl
false ω 𝟘 𝟙 𝟙 ω → refl
false ω 𝟘 𝟙 ω 𝟘 → refl
false ω 𝟘 𝟙 ω 𝟙 → refl
false ω 𝟘 𝟙 ω ω → refl
false ω 𝟘 ω 𝟘 𝟘 → refl
false ω 𝟘 ω 𝟘 𝟙 → refl
false ω 𝟘 ω 𝟘 ω → refl
false ω 𝟘 ω 𝟙 𝟘 → refl
false ω 𝟘 ω 𝟙 𝟙 → refl
false ω 𝟘 ω 𝟙 ω → refl
false ω 𝟘 ω ω 𝟘 → refl
false ω 𝟘 ω ω 𝟙 → refl
false ω 𝟘 ω ω ω → refl
false ω 𝟙 𝟘 𝟘 𝟘 → refl
false ω 𝟙 𝟘 𝟘 𝟙 → refl
false ω 𝟙 𝟘 𝟘 ω → refl
false ω 𝟙 𝟘 𝟙 𝟘 → refl
false ω 𝟙 𝟘 𝟙 𝟙 → refl
false ω 𝟙 𝟘 𝟙 ω → refl
false ω 𝟙 𝟘 ω 𝟘 → refl
false ω 𝟙 𝟘 ω 𝟙 → refl
false ω 𝟙 𝟘 ω ω → refl
false ω 𝟙 𝟙 𝟘 𝟘 → refl
false ω 𝟙 𝟙 𝟘 𝟙 → refl
false ω 𝟙 𝟙 𝟘 ω → refl
false ω 𝟙 𝟙 𝟙 𝟘 → refl
false ω 𝟙 𝟙 𝟙 𝟙 → refl
false ω 𝟙 𝟙 𝟙 ω → refl
false ω 𝟙 𝟙 ω 𝟘 → refl
false ω 𝟙 𝟙 ω 𝟙 → refl
false ω 𝟙 𝟙 ω ω → refl
false ω 𝟙 ω 𝟘 𝟘 → refl
false ω 𝟙 ω 𝟘 𝟙 → refl
false ω 𝟙 ω 𝟘 ω → refl
false ω 𝟙 ω 𝟙 𝟘 → refl
false ω 𝟙 ω 𝟙 𝟙 → refl
false ω 𝟙 ω 𝟙 ω → refl
false ω 𝟙 ω ω 𝟘 → refl
false ω 𝟙 ω ω 𝟙 → refl
false ω 𝟙 ω ω ω → refl
false ω ω 𝟘 𝟘 𝟘 → refl
false ω ω 𝟘 𝟘 𝟙 → refl
false ω ω 𝟘 𝟘 ω → refl
false ω ω 𝟘 𝟙 𝟘 → refl
false ω ω 𝟘 𝟙 𝟙 → refl
false ω ω 𝟘 𝟙 ω → refl
false ω ω 𝟘 ω 𝟘 → refl
false ω ω 𝟘 ω 𝟙 → refl
false ω ω 𝟘 ω ω → refl
false ω ω 𝟙 𝟘 𝟘 → refl
false ω ω 𝟙 𝟘 𝟙 → refl
false ω ω 𝟙 𝟘 ω → refl
false ω ω 𝟙 𝟙 𝟘 → refl
false ω ω 𝟙 𝟙 𝟙 → refl
false ω ω 𝟙 𝟙 ω → refl
false ω ω 𝟙 ω 𝟘 → refl
false ω ω 𝟙 ω 𝟙 → refl
false ω ω 𝟙 ω ω → refl
false ω ω ω 𝟘 𝟘 → refl
false ω ω ω 𝟘 𝟙 → refl
false ω ω ω 𝟘 ω → refl
false ω ω ω 𝟙 𝟘 → refl
false ω ω ω 𝟙 𝟙 → refl
false ω ω ω 𝟙 ω → refl
false ω ω ω ω 𝟘 → refl
false ω ω ω ω 𝟙 → refl
false ω ω ω ω ω → refl
true 𝟘 𝟘 𝟘 𝟘 𝟘 → refl
true 𝟘 𝟘 𝟘 𝟘 𝟙 → refl
true 𝟘 𝟘 𝟘 𝟘 ω → refl
true 𝟘 𝟘 𝟘 𝟙 𝟘 → refl
true 𝟘 𝟘 𝟘 𝟙 𝟙 → refl
true 𝟘 𝟘 𝟘 𝟙 ω → refl
true 𝟘 𝟘 𝟘 ω 𝟘 → refl
true 𝟘 𝟘 𝟘 ω 𝟙 → refl
true 𝟘 𝟘 𝟘 ω ω → refl
true 𝟘 𝟘 𝟙 𝟘 𝟘 → refl
true 𝟘 𝟘 𝟙 𝟘 𝟙 → refl
true 𝟘 𝟘 𝟙 𝟘 ω → refl
true 𝟘 𝟘 𝟙 𝟙 𝟘 → refl
true 𝟘 𝟘 𝟙 𝟙 𝟙 → refl
true 𝟘 𝟘 𝟙 𝟙 ω → refl
true 𝟘 𝟘 𝟙 ω 𝟘 → refl
true 𝟘 𝟘 𝟙 ω 𝟙 → refl
true 𝟘 𝟘 𝟙 ω ω → refl
true 𝟘 𝟘 ω 𝟘 𝟘 → refl
true 𝟘 𝟘 ω 𝟘 𝟙 → refl
true 𝟘 𝟘 ω 𝟘 ω → refl
true 𝟘 𝟘 ω 𝟙 𝟘 → refl
true 𝟘 𝟘 ω 𝟙 𝟙 → refl
true 𝟘 𝟘 ω 𝟙 ω → refl
true 𝟘 𝟘 ω ω 𝟘 → refl
true 𝟘 𝟘 ω ω 𝟙 → refl
true 𝟘 𝟘 ω ω ω → refl
true 𝟘 𝟙 𝟘 𝟘 𝟘 → refl
true 𝟘 𝟙 𝟘 𝟘 𝟙 → refl
true 𝟘 𝟙 𝟘 𝟘 ω → refl
true 𝟘 𝟙 𝟘 𝟙 𝟘 → refl
true 𝟘 𝟙 𝟘 𝟙 𝟙 → refl
true 𝟘 𝟙 𝟘 𝟙 ω → refl
true 𝟘 𝟙 𝟘 ω 𝟘 → refl
true 𝟘 𝟙 𝟘 ω 𝟙 → refl
true 𝟘 𝟙 𝟘 ω ω → refl
true 𝟘 𝟙 𝟙 𝟘 𝟘 → refl
true 𝟘 𝟙 𝟙 𝟘 𝟙 → refl
true 𝟘 𝟙 𝟙 𝟘 ω → refl
true 𝟘 𝟙 𝟙 𝟙 𝟘 → refl
true 𝟘 𝟙 𝟙 𝟙 𝟙 → refl
true 𝟘 𝟙 𝟙 𝟙 ω → refl
true 𝟘 𝟙 𝟙 ω 𝟘 → refl
true 𝟘 𝟙 𝟙 ω 𝟙 → refl
true 𝟘 𝟙 𝟙 ω ω → refl
true 𝟘 𝟙 ω 𝟘 𝟘 → refl
true 𝟘 𝟙 ω 𝟘 𝟙 → refl
true 𝟘 𝟙 ω 𝟘 ω → refl
true 𝟘 𝟙 ω 𝟙 𝟘 → refl
true 𝟘 𝟙 ω 𝟙 𝟙 → refl
true 𝟘 𝟙 ω 𝟙 ω → refl
true 𝟘 𝟙 ω ω 𝟘 → refl
true 𝟘 𝟙 ω ω 𝟙 → refl
true 𝟘 𝟙 ω ω ω → refl
true 𝟘 ω 𝟘 𝟘 𝟘 → refl
true 𝟘 ω 𝟘 𝟘 𝟙 → refl
true 𝟘 ω 𝟘 𝟘 ω → refl
true 𝟘 ω 𝟘 𝟙 𝟘 → refl
true 𝟘 ω 𝟘 𝟙 𝟙 → refl
true 𝟘 ω 𝟘 𝟙 ω → refl
true 𝟘 ω 𝟘 ω 𝟘 → refl
true 𝟘 ω 𝟘 ω 𝟙 → refl
true 𝟘 ω 𝟘 ω ω → refl
true 𝟘 ω 𝟙 𝟘 𝟘 → refl
true 𝟘 ω 𝟙 𝟘 𝟙 → refl
true 𝟘 ω 𝟙 𝟘 ω → refl
true 𝟘 ω 𝟙 𝟙 𝟘 → refl
true 𝟘 ω 𝟙 𝟙 𝟙 → refl
true 𝟘 ω 𝟙 𝟙 ω → refl
true 𝟘 ω 𝟙 ω 𝟘 → refl
true 𝟘 ω 𝟙 ω 𝟙 → refl
true 𝟘 ω 𝟙 ω ω → refl
true 𝟘 ω ω 𝟘 𝟘 → refl
true 𝟘 ω ω 𝟘 𝟙 → refl
true 𝟘 ω ω 𝟘 ω → refl
true 𝟘 ω ω 𝟙 𝟘 → refl
true 𝟘 ω ω 𝟙 𝟙 → refl
true 𝟘 ω ω 𝟙 ω → refl
true 𝟘 ω ω ω 𝟘 → refl
true 𝟘 ω ω ω 𝟙 → refl
true 𝟘 ω ω ω ω → refl
true 𝟙 𝟘 𝟘 𝟘 𝟘 → refl
true 𝟙 𝟘 𝟘 𝟘 𝟙 → refl
true 𝟙 𝟘 𝟘 𝟘 ω → refl
true 𝟙 𝟘 𝟘 𝟙 𝟘 → refl
true 𝟙 𝟘 𝟘 𝟙 𝟙 → refl
true 𝟙 𝟘 𝟘 𝟙 ω → refl
true 𝟙 𝟘 𝟘 ω 𝟘 → refl
true 𝟙 𝟘 𝟘 ω 𝟙 → refl
true 𝟙 𝟘 𝟘 ω ω → refl
true 𝟙 𝟘 𝟙 𝟘 𝟘 → refl
true 𝟙 𝟘 𝟙 𝟘 𝟙 → refl
true 𝟙 𝟘 𝟙 𝟘 ω → refl
true 𝟙 𝟘 𝟙 𝟙 𝟘 → refl
true 𝟙 𝟘 𝟙 𝟙 𝟙 → refl
true 𝟙 𝟘 𝟙 𝟙 ω → refl
true 𝟙 𝟘 𝟙 ω 𝟘 → refl
true 𝟙 𝟘 𝟙 ω 𝟙 → refl
true 𝟙 𝟘 𝟙 ω ω → refl
true 𝟙 𝟘 ω 𝟘 𝟘 → refl
true 𝟙 𝟘 ω 𝟘 𝟙 → refl
true 𝟙 𝟘 ω 𝟘 ω → refl
true 𝟙 𝟘 ω 𝟙 𝟘 → refl
true 𝟙 𝟘 ω 𝟙 𝟙 → refl
true 𝟙 𝟘 ω 𝟙 ω → refl
true 𝟙 𝟘 ω ω 𝟘 → refl
true 𝟙 𝟘 ω ω 𝟙 → refl
true 𝟙 𝟘 ω ω ω → refl
true 𝟙 𝟙 𝟘 𝟘 𝟘 → refl
true 𝟙 𝟙 𝟘 𝟘 𝟙 → refl
true 𝟙 𝟙 𝟘 𝟘 ω → refl
true 𝟙 𝟙 𝟘 𝟙 𝟘 → refl
true 𝟙 𝟙 𝟘 𝟙 𝟙 → refl
true 𝟙 𝟙 𝟘 𝟙 ω → refl
true 𝟙 𝟙 𝟘 ω 𝟘 → refl
true 𝟙 𝟙 𝟘 ω 𝟙 → refl
true 𝟙 𝟙 𝟘 ω ω → refl
true 𝟙 𝟙 𝟙 𝟘 𝟘 → refl
true 𝟙 𝟙 𝟙 𝟘 𝟙 → refl
true 𝟙 𝟙 𝟙 𝟘 ω → refl
true 𝟙 𝟙 𝟙 𝟙 𝟘 → refl
true 𝟙 𝟙 𝟙 𝟙 𝟙 → refl
true 𝟙 𝟙 𝟙 𝟙 ω → refl
true 𝟙 𝟙 𝟙 ω 𝟘 → refl
true 𝟙 𝟙 𝟙 ω 𝟙 → refl
true 𝟙 𝟙 𝟙 ω ω → refl
true 𝟙 𝟙 ω 𝟘 𝟘 → refl
true 𝟙 𝟙 ω 𝟘 𝟙 → refl
true 𝟙 𝟙 ω 𝟘 ω → refl
true 𝟙 𝟙 ω 𝟙 𝟘 → refl
true 𝟙 𝟙 ω 𝟙 𝟙 → refl
true 𝟙 𝟙 ω 𝟙 ω → refl
true 𝟙 𝟙 ω ω 𝟘 → refl
true 𝟙 𝟙 ω ω 𝟙 → refl
true 𝟙 𝟙 ω ω ω → refl
true 𝟙 ω 𝟘 𝟘 𝟘 → refl
true 𝟙 ω 𝟘 𝟘 𝟙 → refl
true 𝟙 ω 𝟘 𝟘 ω → refl
true 𝟙 ω 𝟘 𝟙 𝟘 → refl
true 𝟙 ω 𝟘 𝟙 𝟙 → refl
true 𝟙 ω 𝟘 𝟙 ω → refl
true 𝟙 ω 𝟘 ω 𝟘 → refl
true 𝟙 ω 𝟘 ω 𝟙 → refl
true 𝟙 ω 𝟘 ω ω → refl
true 𝟙 ω 𝟙 𝟘 𝟘 → refl
true 𝟙 ω 𝟙 𝟘 𝟙 → refl
true 𝟙 ω 𝟙 𝟘 ω → refl
true 𝟙 ω 𝟙 𝟙 𝟘 → refl
true 𝟙 ω 𝟙 𝟙 𝟙 → refl
true 𝟙 ω 𝟙 𝟙 ω → refl
true 𝟙 ω 𝟙 ω 𝟘 → refl
true 𝟙 ω 𝟙 ω 𝟙 → refl
true 𝟙 ω 𝟙 ω ω → refl
true 𝟙 ω ω 𝟘 𝟘 → refl
true 𝟙 ω ω 𝟘 𝟙 → refl
true 𝟙 ω ω 𝟘 ω → refl
true 𝟙 ω ω 𝟙 𝟘 → refl
true 𝟙 ω ω 𝟙 𝟙 → refl
true 𝟙 ω ω 𝟙 ω → refl
true 𝟙 ω ω ω 𝟘 → refl
true 𝟙 ω ω ω 𝟙 → refl
true 𝟙 ω ω ω ω → refl
true ω 𝟘 𝟘 𝟘 𝟘 → refl
true ω 𝟘 𝟘 𝟘 𝟙 → refl
true ω 𝟘 𝟘 𝟘 ω → refl
true ω 𝟘 𝟘 𝟙 𝟘 → refl
true ω 𝟘 𝟘 𝟙 𝟙 → refl
true ω 𝟘 𝟘 𝟙 ω → refl
true ω 𝟘 𝟘 ω 𝟘 → refl
true ω 𝟘 𝟘 ω 𝟙 → refl
true ω 𝟘 𝟘 ω ω → refl
true ω 𝟘 𝟙 𝟘 𝟘 → refl
true ω 𝟘 𝟙 𝟘 𝟙 → refl
true ω 𝟘 𝟙 𝟘 ω → refl
true ω 𝟘 𝟙 𝟙 𝟘 → refl
true ω 𝟘 𝟙 𝟙 𝟙 → refl
true ω 𝟘 𝟙 𝟙 ω → refl
true ω 𝟘 𝟙 ω 𝟘 → refl
true ω 𝟘 𝟙 ω 𝟙 → refl
true ω 𝟘 𝟙 ω ω → refl
true ω 𝟘 ω 𝟘 𝟘 → refl
true ω 𝟘 ω 𝟘 𝟙 → refl
true ω 𝟘 ω 𝟘 ω → refl
true ω 𝟘 ω 𝟙 𝟘 → refl
true ω 𝟘 ω 𝟙 𝟙 → refl
true ω 𝟘 ω 𝟙 ω → refl
true ω 𝟘 ω ω 𝟘 → refl
true ω 𝟘 ω ω 𝟙 → refl
true ω 𝟘 ω ω ω → refl
true ω 𝟙 𝟘 𝟘 𝟘 → refl
true ω 𝟙 𝟘 𝟘 𝟙 → refl
true ω 𝟙 𝟘 𝟘 ω → refl
true ω 𝟙 𝟘 𝟙 𝟘 → refl
true ω 𝟙 𝟘 𝟙 𝟙 → refl
true ω 𝟙 𝟘 𝟙 ω → refl
true ω 𝟙 𝟘 ω 𝟘 → refl
true ω 𝟙 𝟘 ω 𝟙 → refl
true ω 𝟙 𝟘 ω ω → refl
true ω 𝟙 𝟙 𝟘 𝟘 → refl
true ω 𝟙 𝟙 𝟘 𝟙 → refl
true ω 𝟙 𝟙 𝟘 ω → refl
true ω 𝟙 𝟙 𝟙 𝟘 → refl
true ω 𝟙 𝟙 𝟙 𝟙 → refl
true ω 𝟙 𝟙 𝟙 ω → refl
true ω 𝟙 𝟙 ω 𝟘 → refl
true ω 𝟙 𝟙 ω 𝟙 → refl
true ω 𝟙 𝟙 ω ω → refl
true ω 𝟙 ω 𝟘 𝟘 → refl
true ω 𝟙 ω 𝟘 𝟙 → refl
true ω 𝟙 ω 𝟘 ω → refl
true ω 𝟙 ω 𝟙 𝟘 → refl
true ω 𝟙 ω 𝟙 𝟙 → refl
true ω 𝟙 ω 𝟙 ω → refl
true ω 𝟙 ω ω 𝟘 → refl
true ω 𝟙 ω ω 𝟙 → refl
true ω 𝟙 ω ω ω → refl
true ω ω 𝟘 𝟘 𝟘 → refl
true ω ω 𝟘 𝟘 𝟙 → refl
true ω ω 𝟘 𝟘 ω → refl
true ω ω 𝟘 𝟙 𝟘 → refl
true ω ω 𝟘 𝟙 𝟙 → refl
true ω ω 𝟘 𝟙 ω → refl
true ω ω 𝟘 ω 𝟘 → refl
true ω ω 𝟘 ω 𝟙 → refl
true ω ω 𝟘 ω ω → refl
true ω ω 𝟙 𝟘 𝟘 → refl
true ω ω 𝟙 𝟘 𝟙 → refl
true ω ω 𝟙 𝟘 ω → refl
true ω ω 𝟙 𝟙 𝟘 → refl
true ω ω 𝟙 𝟙 𝟙 → refl
true ω ω 𝟙 𝟙 ω → refl
true ω ω 𝟙 ω 𝟘 → refl
true ω ω 𝟙 ω 𝟙 → refl
true ω ω 𝟙 ω ω → refl
true ω ω ω 𝟘 𝟘 → refl
true ω ω ω 𝟘 𝟙 → refl
true ω ω ω 𝟘 ω → refl
true ω ω ω 𝟙 𝟘 → refl
true ω ω ω 𝟙 𝟙 → refl
true ω ω ω 𝟙 ω → refl
true ω ω ω ω 𝟘 → refl
true ω ω ω ω 𝟙 → refl
true ω ω ω ω ω → refl
opaque
zero-one-many⇒erasure-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(zero-one-many-modality 𝟙≤𝟘 v₁)
(ErasureModality v₂)
zero-one-many→erasure
zero-one-many⇒erasure-no-nr-preserving {v₂ = record{}} {𝟙≤𝟘} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ (ZOM.zero-one-many-has-well-behaved-zero 𝟙≤𝟘)
where
open Is-no-nr-preserving-morphism
opaque
zero-one-many⇒erasure-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(zero-one-many-modality 𝟙≤𝟘 v₁)
(ErasureModality v₂)
zero-one-many→erasure
zero-one-many⇒erasure-no-nr-glb-preserving {v₂} = λ where
.tr-nrᵢ-GLB _ → EP.Erasure-nrᵢ-glb v₂ _ _ _
.tr-nrᵢ-𝟙-GLB _ → EP.Erasure-nrᵢ-glb v₂ _ _ _
where
open Is-no-nr-glb-preserving-morphism
opaque
erasure⇒linearity-nr-preserving :
Is-nr-preserving-morphism
(ErasureModality v₁)
(linearityModality v₂)
⦃ E.erasure-has-nr ⦄
⦃ L.zero-one-many-has-nr ⦄
erasure→zero-one-many
erasure⇒linearity-nr-preserving = erasure⇨zero-one-many-nr-preserving
opaque
erasure⇒affine-nr-preserving :
Is-nr-preserving-morphism
(ErasureModality v₁)
(affineModality v₂)
⦃ E.erasure-has-nr ⦄
⦃ A.zero-one-many-has-nr ⦄
erasure→zero-one-many
erasure⇒affine-nr-preserving = erasure⇨zero-one-many-nr-preserving
opaque
erasure⇒linearity-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(ErasureModality v₁)
(linearityModality v₂)
erasure→zero-one-many
erasure⇒linearity-no-nr-preserving = erasure⇨zero-one-many-no-nr-preserving
opaque
erasure⇒affine-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(ErasureModality v₁)
(affineModality v₂)
erasure→zero-one-many
erasure⇒affine-no-nr-preserving = erasure⇨zero-one-many-no-nr-preserving
opaque
erasure⇒linearity-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(ErasureModality v₁)
(linearityModality v₂)
erasure→zero-one-many
erasure⇒linearity-no-nr-glb-preserving = erasure⇨zero-one-many-no-nr-glb-preserving
opaque
erasure⇒affine-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(ErasureModality v₁)
(affineModality v₂)
erasure→zero-one-many
erasure⇒affine-no-nr-glb-preserving = erasure⇨zero-one-many-no-nr-glb-preserving
opaque
linearity⇒erasure-nr-preserving :
Is-nr-preserving-morphism
(linearityModality v₂)
(ErasureModality v₁)
⦃ L.zero-one-many-has-nr ⦄
⦃ E.erasure-has-nr ⦄
zero-one-many→erasure
linearity⇒erasure-nr-preserving = zero-one-many⇒erasure-nr-preserving
opaque
affine⇒erasure-nr-preserving :
Is-nr-preserving-morphism
(affineModality v₂)
(ErasureModality v₁)
⦃ A.zero-one-many-has-nr ⦄
⦃ E.erasure-has-nr ⦄
zero-one-many→erasure
affine⇒erasure-nr-preserving = zero-one-many⇒erasure-nr-preserving
opaque
linearity⇒erasure-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(linearityModality v₁)
(ErasureModality v₂)
zero-one-many→erasure
linearity⇒erasure-no-nr-preserving = zero-one-many⇒erasure-no-nr-preserving
opaque
affine⇒erasure-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(affineModality v₁)
(ErasureModality v₂)
zero-one-many→erasure
affine⇒erasure-no-nr-preserving = zero-one-many⇒erasure-no-nr-preserving
opaque
linearity⇒erasure-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(linearityModality v₁)
(ErasureModality v₂)
zero-one-many→erasure
linearity⇒erasure-no-nr-glb-preserving = zero-one-many⇒erasure-no-nr-glb-preserving
opaque
affine⇒erasure-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(affineModality v₁)
(ErasureModality v₂)
zero-one-many→erasure
affine⇒erasure-no-nr-glb-preserving = zero-one-many⇒erasure-no-nr-glb-preserving
opaque
linearity⇨linear-or-affine-nr-preserving :
Is-nr-preserving-morphism
(linearityModality v₁)
(linear-or-affine v₂)
⦃ L.zero-one-many-has-nr ⦄
⦃ LA.linear-or-affine-has-nr ⦄
linearity→linear-or-affine
linearity⇨linear-or-affine-nr-preserving = λ where
.tr-nr {r} → tr-nr′ _ r _ _ _
where
open Is-nr-preserving-morphism
tr : Linearity → Linear-or-affine
tr = linearity→linear-or-affine
tr-nr′ :
∀ p r z s n →
tr (L.nr p r z s n) LA.≤
LA.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ω → refl
𝟘 𝟘 𝟘 ω 𝟘 → refl
𝟘 𝟘 𝟘 ω 𝟙 → refl
𝟘 𝟘 𝟘 ω ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ω → refl
𝟘 𝟘 𝟙 ω 𝟘 → refl
𝟘 𝟘 𝟙 ω 𝟙 → refl
𝟘 𝟘 𝟙 ω ω → refl
𝟘 𝟘 ω 𝟘 𝟘 → refl
𝟘 𝟘 ω 𝟘 𝟙 → refl
𝟘 𝟘 ω 𝟘 ω → refl
𝟘 𝟘 ω 𝟙 𝟘 → refl
𝟘 𝟘 ω 𝟙 𝟙 → refl
𝟘 𝟘 ω 𝟙 ω → refl
𝟘 𝟘 ω ω 𝟘 → refl
𝟘 𝟘 ω ω 𝟙 → refl
𝟘 𝟘 ω ω ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ω → refl
𝟘 𝟙 𝟘 ω 𝟘 → refl
𝟘 𝟙 𝟘 ω 𝟙 → refl
𝟘 𝟙 𝟘 ω ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ω → refl
𝟘 𝟙 𝟙 ω 𝟘 → refl
𝟘 𝟙 𝟙 ω 𝟙 → refl
𝟘 𝟙 𝟙 ω ω → refl
𝟘 𝟙 ω 𝟘 𝟘 → refl
𝟘 𝟙 ω 𝟘 𝟙 → refl
𝟘 𝟙 ω 𝟘 ω → refl
𝟘 𝟙 ω 𝟙 𝟘 → refl
𝟘 𝟙 ω 𝟙 𝟙 → refl
𝟘 𝟙 ω 𝟙 ω → refl
𝟘 𝟙 ω ω 𝟘 → refl
𝟘 𝟙 ω ω 𝟙 → refl
𝟘 𝟙 ω ω ω → refl
𝟘 ω 𝟘 𝟘 𝟘 → refl
𝟘 ω 𝟘 𝟘 𝟙 → refl
𝟘 ω 𝟘 𝟘 ω → refl
𝟘 ω 𝟘 𝟙 𝟘 → refl
𝟘 ω 𝟘 𝟙 𝟙 → refl
𝟘 ω 𝟘 𝟙 ω → refl
𝟘 ω 𝟘 ω 𝟘 → refl
𝟘 ω 𝟘 ω 𝟙 → refl
𝟘 ω 𝟘 ω ω → refl
𝟘 ω 𝟙 𝟘 𝟘 → refl
𝟘 ω 𝟙 𝟘 𝟙 → refl
𝟘 ω 𝟙 𝟘 ω → refl
𝟘 ω 𝟙 𝟙 𝟘 → refl
𝟘 ω 𝟙 𝟙 𝟙 → refl
𝟘 ω 𝟙 𝟙 ω → refl
𝟘 ω 𝟙 ω 𝟘 → refl
𝟘 ω 𝟙 ω 𝟙 → refl
𝟘 ω 𝟙 ω ω → refl
𝟘 ω ω 𝟘 𝟘 → refl
𝟘 ω ω 𝟘 𝟙 → refl
𝟘 ω ω 𝟘 ω → refl
𝟘 ω ω 𝟙 𝟘 → refl
𝟘 ω ω 𝟙 𝟙 → refl
𝟘 ω ω 𝟙 ω → refl
𝟘 ω ω ω 𝟘 → refl
𝟘 ω ω ω 𝟙 → refl
𝟘 ω ω ω ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ω → refl
𝟙 𝟘 𝟘 ω 𝟘 → refl
𝟙 𝟘 𝟘 ω 𝟙 → refl
𝟙 𝟘 𝟘 ω ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ω → refl
𝟙 𝟘 𝟙 ω 𝟘 → refl
𝟙 𝟘 𝟙 ω 𝟙 → refl
𝟙 𝟘 𝟙 ω ω → refl
𝟙 𝟘 ω 𝟘 𝟘 → refl
𝟙 𝟘 ω 𝟘 𝟙 → refl
𝟙 𝟘 ω 𝟘 ω → refl
𝟙 𝟘 ω 𝟙 𝟘 → refl
𝟙 𝟘 ω 𝟙 𝟙 → refl
𝟙 𝟘 ω 𝟙 ω → refl
𝟙 𝟘 ω ω 𝟘 → refl
𝟙 𝟘 ω ω 𝟙 → refl
𝟙 𝟘 ω ω ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ω → refl
𝟙 𝟙 𝟘 ω 𝟘 → refl
𝟙 𝟙 𝟘 ω 𝟙 → refl
𝟙 𝟙 𝟘 ω ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ω → refl
𝟙 𝟙 𝟙 ω 𝟘 → refl
𝟙 𝟙 𝟙 ω 𝟙 → refl
𝟙 𝟙 𝟙 ω ω → refl
𝟙 𝟙 ω 𝟘 𝟘 → refl
𝟙 𝟙 ω 𝟘 𝟙 → refl
𝟙 𝟙 ω 𝟘 ω → refl
𝟙 𝟙 ω 𝟙 𝟘 → refl
𝟙 𝟙 ω 𝟙 𝟙 → refl
𝟙 𝟙 ω 𝟙 ω → refl
𝟙 𝟙 ω ω 𝟘 → refl
𝟙 𝟙 ω ω 𝟙 → refl
𝟙 𝟙 ω ω ω → refl
𝟙 ω 𝟘 𝟘 𝟘 → refl
𝟙 ω 𝟘 𝟘 𝟙 → refl
𝟙 ω 𝟘 𝟘 ω → refl
𝟙 ω 𝟘 𝟙 𝟘 → refl
𝟙 ω 𝟘 𝟙 𝟙 → refl
𝟙 ω 𝟘 𝟙 ω → refl
𝟙 ω 𝟘 ω 𝟘 → refl
𝟙 ω 𝟘 ω 𝟙 → refl
𝟙 ω 𝟘 ω ω → refl
𝟙 ω 𝟙 𝟘 𝟘 → refl
𝟙 ω 𝟙 𝟘 𝟙 → refl
𝟙 ω 𝟙 𝟘 ω → refl
𝟙 ω 𝟙 𝟙 𝟘 → refl
𝟙 ω 𝟙 𝟙 𝟙 → refl
𝟙 ω 𝟙 𝟙 ω → refl
𝟙 ω 𝟙 ω 𝟘 → refl
𝟙 ω 𝟙 ω 𝟙 → refl
𝟙 ω 𝟙 ω ω → refl
𝟙 ω ω 𝟘 𝟘 → refl
𝟙 ω ω 𝟘 𝟙 → refl
𝟙 ω ω 𝟘 ω → refl
𝟙 ω ω 𝟙 𝟘 → refl
𝟙 ω ω 𝟙 𝟙 → refl
𝟙 ω ω 𝟙 ω → refl
𝟙 ω ω ω 𝟘 → refl
𝟙 ω ω ω 𝟙 → refl
𝟙 ω ω ω ω → refl
ω 𝟘 𝟘 𝟘 𝟘 → refl
ω 𝟘 𝟘 𝟘 𝟙 → refl
ω 𝟘 𝟘 𝟘 ω → refl
ω 𝟘 𝟘 𝟙 𝟘 → refl
ω 𝟘 𝟘 𝟙 𝟙 → refl
ω 𝟘 𝟘 𝟙 ω → refl
ω 𝟘 𝟘 ω 𝟘 → refl
ω 𝟘 𝟘 ω 𝟙 → refl
ω 𝟘 𝟘 ω ω → refl
ω 𝟘 𝟙 𝟘 𝟘 → refl
ω 𝟘 𝟙 𝟘 𝟙 → refl
ω 𝟘 𝟙 𝟘 ω → refl
ω 𝟘 𝟙 𝟙 𝟘 → refl
ω 𝟘 𝟙 𝟙 𝟙 → refl
ω 𝟘 𝟙 𝟙 ω → refl
ω 𝟘 𝟙 ω 𝟘 → refl
ω 𝟘 𝟙 ω 𝟙 → refl
ω 𝟘 𝟙 ω ω → refl
ω 𝟘 ω 𝟘 𝟘 → refl
ω 𝟘 ω 𝟘 𝟙 → refl
ω 𝟘 ω 𝟘 ω → refl
ω 𝟘 ω 𝟙 𝟘 → refl
ω 𝟘 ω 𝟙 𝟙 → refl
ω 𝟘 ω 𝟙 ω → refl
ω 𝟘 ω ω 𝟘 → refl
ω 𝟘 ω ω 𝟙 → refl
ω 𝟘 ω ω ω → refl
ω 𝟙 𝟘 𝟘 𝟘 → refl
ω 𝟙 𝟘 𝟘 𝟙 → refl
ω 𝟙 𝟘 𝟘 ω → refl
ω 𝟙 𝟘 𝟙 𝟘 → refl
ω 𝟙 𝟘 𝟙 𝟙 → refl
ω 𝟙 𝟘 𝟙 ω → refl
ω 𝟙 𝟘 ω 𝟘 → refl
ω 𝟙 𝟘 ω 𝟙 → refl
ω 𝟙 𝟘 ω ω → refl
ω 𝟙 𝟙 𝟘 𝟘 → refl
ω 𝟙 𝟙 𝟘 𝟙 → refl
ω 𝟙 𝟙 𝟘 ω → refl
ω 𝟙 𝟙 𝟙 𝟘 → refl
ω 𝟙 𝟙 𝟙 𝟙 → refl
ω 𝟙 𝟙 𝟙 ω → refl
ω 𝟙 𝟙 ω 𝟘 → refl
ω 𝟙 𝟙 ω 𝟙 → refl
ω 𝟙 𝟙 ω ω → refl
ω 𝟙 ω 𝟘 𝟘 → refl
ω 𝟙 ω 𝟘 𝟙 → refl
ω 𝟙 ω 𝟘 ω → refl
ω 𝟙 ω 𝟙 𝟘 → refl
ω 𝟙 ω 𝟙 𝟙 → refl
ω 𝟙 ω 𝟙 ω → refl
ω 𝟙 ω ω 𝟘 → refl
ω 𝟙 ω ω 𝟙 → refl
ω 𝟙 ω ω ω → refl
ω ω 𝟘 𝟘 𝟘 → refl
ω ω 𝟘 𝟘 𝟙 → refl
ω ω 𝟘 𝟘 ω → refl
ω ω 𝟘 𝟙 𝟘 → refl
ω ω 𝟘 𝟙 𝟙 → refl
ω ω 𝟘 𝟙 ω → refl
ω ω 𝟘 ω 𝟘 → refl
ω ω 𝟘 ω 𝟙 → refl
ω ω 𝟘 ω ω → refl
ω ω 𝟙 𝟘 𝟘 → refl
ω ω 𝟙 𝟘 𝟙 → refl
ω ω 𝟙 𝟘 ω → refl
ω ω 𝟙 𝟙 𝟘 → refl
ω ω 𝟙 𝟙 𝟙 → refl
ω ω 𝟙 𝟙 ω → refl
ω ω 𝟙 ω 𝟘 → refl
ω ω 𝟙 ω 𝟙 → refl
ω ω 𝟙 ω ω → refl
ω ω ω 𝟘 𝟘 → refl
ω ω ω 𝟘 𝟙 → refl
ω ω ω 𝟘 ω → refl
ω ω ω 𝟙 𝟘 → refl
ω ω ω 𝟙 𝟙 → refl
ω ω ω 𝟙 ω → refl
ω ω ω ω 𝟘 → refl
ω ω ω ω 𝟙 → refl
ω ω ω ω ω → refl
opaque
linearity⇨linear-or-affine-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(linearityModality v₁)
(linear-or-affine v₂)
linearity→linear-or-affine
linearity⇨linear-or-affine-no-nr-preserving {v₁ = v₁@record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ (L.linearity-has-well-behaved-zero v₁)
where
open Is-no-nr-preserving-morphism
opaque
linearity⇨linear-or-affine-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(linearityModality v₁)
(linear-or-affine v₂)
linearity→linear-or-affine
linearity⇨linear-or-affine-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , LA.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , LA.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
linear-or-affine⇨linearity-nr-preserving :
Is-nr-preserving-morphism
(linear-or-affine v₁)
(linearityModality v₂)
⦃ LA.linear-or-affine-has-nr ⦄
⦃ L.zero-one-many-has-nr ⦄
linear-or-affine→linearity
linear-or-affine⇨linearity-nr-preserving {v₂} = λ where
.tr-nr {r} → ≤-reflexive (tr-nr′ _ r _ _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (linearityModality v₂)
tr : Linear-or-affine → Linearity
tr = linear-or-affine→linearity
tr-nr′ :
∀ p r z s n →
tr (LA.nr p r z s n) ≡
L.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ≤𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ≤ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ≤ω → refl
𝟘 𝟘 𝟘 ≤𝟙 𝟘 → refl
𝟘 𝟘 𝟘 ≤𝟙 𝟙 → refl
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟘 ≤𝟙 ≤ω → refl
𝟘 𝟘 𝟘 ≤ω 𝟘 → refl
𝟘 𝟘 𝟘 ≤ω 𝟙 → refl
𝟘 𝟘 𝟘 ≤ω ≤𝟙 → refl
𝟘 𝟘 𝟘 ≤ω ≤ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ≤ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ≤ω → refl
𝟘 𝟘 𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟘 𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟘 𝟙 ≤ω 𝟘 → refl
𝟘 𝟘 𝟙 ≤ω 𝟙 → refl
𝟘 𝟘 𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟘 𝟙 ≤ω ≤ω → refl
𝟘 𝟘 ≤𝟙 𝟘 𝟘 → refl
𝟘 𝟘 ≤𝟙 𝟘 𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟘 ≤ω → refl
𝟘 𝟘 ≤𝟙 𝟙 𝟘 → refl
𝟘 𝟘 ≤𝟙 𝟙 𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟙 ≤ω → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟘 ≤𝟙 ≤ω 𝟘 → refl
𝟘 𝟘 ≤𝟙 ≤ω 𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤ω ≤ω → refl
𝟘 𝟘 ≤ω 𝟘 𝟘 → refl
𝟘 𝟘 ≤ω 𝟘 𝟙 → refl
𝟘 𝟘 ≤ω 𝟘 ≤𝟙 → refl
𝟘 𝟘 ≤ω 𝟘 ≤ω → refl
𝟘 𝟘 ≤ω 𝟙 𝟘 → refl
𝟘 𝟘 ≤ω 𝟙 𝟙 → refl
𝟘 𝟘 ≤ω 𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤ω 𝟙 ≤ω → refl
𝟘 𝟘 ≤ω ≤𝟙 𝟘 → refl
𝟘 𝟘 ≤ω ≤𝟙 𝟙 → refl
𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤ω ≤𝟙 ≤ω → refl
𝟘 𝟘 ≤ω ≤ω 𝟘 → refl
𝟘 𝟘 ≤ω ≤ω 𝟙 → refl
𝟘 𝟘 ≤ω ≤ω ≤𝟙 → refl
𝟘 𝟘 ≤ω ≤ω ≤ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ≤ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ≤ω → refl
𝟘 𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟘 𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟘 𝟙 𝟘 ≤ω 𝟘 → refl
𝟘 𝟙 𝟘 ≤ω 𝟙 → refl
𝟘 𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟘 𝟙 𝟘 ≤ω ≤ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ≤ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ≤ω → refl
𝟘 𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟙 𝟙 ≤ω 𝟘 → refl
𝟘 𝟙 𝟙 ≤ω 𝟙 → refl
𝟘 𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟙 𝟙 ≤ω ≤ω → refl
𝟘 𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟘 𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟘 𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟘 𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟘 𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟘 𝟙 ≤ω 𝟘 𝟘 → refl
𝟘 𝟙 ≤ω 𝟘 𝟙 → refl
𝟘 𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟘 𝟙 ≤ω 𝟘 ≤ω → refl
𝟘 𝟙 ≤ω 𝟙 𝟘 → refl
𝟘 𝟙 ≤ω 𝟙 𝟙 → refl
𝟘 𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤ω 𝟙 ≤ω → refl
𝟘 𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟘 𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟘 𝟙 ≤ω ≤ω 𝟘 → refl
𝟘 𝟙 ≤ω ≤ω 𝟙 → refl
𝟘 𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟘 𝟙 ≤ω ≤ω ≤ω → refl
𝟘 ≤𝟙 𝟘 𝟘 𝟘 → refl
𝟘 ≤𝟙 𝟘 𝟘 𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟘 ≤ω → refl
𝟘 ≤𝟙 𝟘 𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟘 𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟘 ≤ω 𝟘 → refl
𝟘 ≤𝟙 𝟘 ≤ω 𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤ω ≤ω → refl
𝟘 ≤𝟙 𝟙 𝟘 𝟘 → refl
𝟘 ≤𝟙 𝟙 𝟘 𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟘 ≤ω → refl
𝟘 ≤𝟙 𝟙 𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟙 𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟙 ≤ω 𝟘 → refl
𝟘 ≤𝟙 𝟙 ≤ω 𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤ω ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟘 ≤𝟙 ≤ω 𝟘 𝟘 → refl
𝟘 ≤𝟙 ≤ω 𝟘 𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟘 ≤ω → refl
𝟘 ≤𝟙 ≤ω 𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤ω 𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤ω ≤ω 𝟘 → refl
𝟘 ≤𝟙 ≤ω ≤ω 𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤ω ≤ω → refl
𝟘 ≤ω 𝟘 𝟘 𝟘 → refl
𝟘 ≤ω 𝟘 𝟘 𝟙 → refl
𝟘 ≤ω 𝟘 𝟘 ≤𝟙 → refl
𝟘 ≤ω 𝟘 𝟘 ≤ω → refl
𝟘 ≤ω 𝟘 𝟙 𝟘 → refl
𝟘 ≤ω 𝟘 𝟙 𝟙 → refl
𝟘 ≤ω 𝟘 𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟘 𝟙 ≤ω → refl
𝟘 ≤ω 𝟘 ≤𝟙 𝟘 → refl
𝟘 ≤ω 𝟘 ≤𝟙 𝟙 → refl
𝟘 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟘 ≤𝟙 ≤ω → refl
𝟘 ≤ω 𝟘 ≤ω 𝟘 → refl
𝟘 ≤ω 𝟘 ≤ω 𝟙 → refl
𝟘 ≤ω 𝟘 ≤ω ≤𝟙 → refl
𝟘 ≤ω 𝟘 ≤ω ≤ω → refl
𝟘 ≤ω 𝟙 𝟘 𝟘 → refl
𝟘 ≤ω 𝟙 𝟘 𝟙 → refl
𝟘 ≤ω 𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤ω 𝟙 𝟘 ≤ω → refl
𝟘 ≤ω 𝟙 𝟙 𝟘 → refl
𝟘 ≤ω 𝟙 𝟙 𝟙 → refl
𝟘 ≤ω 𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟙 𝟙 ≤ω → refl
𝟘 ≤ω 𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤ω 𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤ω 𝟙 ≤ω 𝟘 → refl
𝟘 ≤ω 𝟙 ≤ω 𝟙 → refl
𝟘 ≤ω 𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤ω 𝟙 ≤ω ≤ω → refl
𝟘 ≤ω ≤𝟙 𝟘 𝟘 → refl
𝟘 ≤ω ≤𝟙 𝟘 𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟘 ≤ω → refl
𝟘 ≤ω ≤𝟙 𝟙 𝟘 → refl
𝟘 ≤ω ≤𝟙 𝟙 𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟙 ≤ω → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤ω ≤𝟙 ≤ω 𝟘 → refl
𝟘 ≤ω ≤𝟙 ≤ω 𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤ω ≤ω → refl
𝟘 ≤ω ≤ω 𝟘 𝟘 → refl
𝟘 ≤ω ≤ω 𝟘 𝟙 → refl
𝟘 ≤ω ≤ω 𝟘 ≤𝟙 → refl
𝟘 ≤ω ≤ω 𝟘 ≤ω → refl
𝟘 ≤ω ≤ω 𝟙 𝟘 → refl
𝟘 ≤ω ≤ω 𝟙 𝟙 → refl
𝟘 ≤ω ≤ω 𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤ω 𝟙 ≤ω → refl
𝟘 ≤ω ≤ω ≤𝟙 𝟘 → refl
𝟘 ≤ω ≤ω ≤𝟙 𝟙 → refl
𝟘 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤ω ≤𝟙 ≤ω → refl
𝟘 ≤ω ≤ω ≤ω 𝟘 → refl
𝟘 ≤ω ≤ω ≤ω 𝟙 → refl
𝟘 ≤ω ≤ω ≤ω ≤𝟙 → refl
𝟘 ≤ω ≤ω ≤ω ≤ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ≤𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ≤ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ≤ω → refl
𝟙 𝟘 𝟘 ≤𝟙 𝟘 → refl
𝟙 𝟘 𝟘 ≤𝟙 𝟙 → refl
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟘 ≤𝟙 ≤ω → refl
𝟙 𝟘 𝟘 ≤ω 𝟘 → refl
𝟙 𝟘 𝟘 ≤ω 𝟙 → refl
𝟙 𝟘 𝟘 ≤ω ≤𝟙 → refl
𝟙 𝟘 𝟘 ≤ω ≤ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ≤ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ≤ω → refl
𝟙 𝟘 𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟘 𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟘 𝟙 ≤ω 𝟘 → refl
𝟙 𝟘 𝟙 ≤ω 𝟙 → refl
𝟙 𝟘 𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟘 𝟙 ≤ω ≤ω → refl
𝟙 𝟘 ≤𝟙 𝟘 𝟘 → refl
𝟙 𝟘 ≤𝟙 𝟘 𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟘 ≤ω → refl
𝟙 𝟘 ≤𝟙 𝟙 𝟘 → refl
𝟙 𝟘 ≤𝟙 𝟙 𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟙 ≤ω → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟘 ≤𝟙 ≤ω 𝟘 → refl
𝟙 𝟘 ≤𝟙 ≤ω 𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤ω ≤ω → refl
𝟙 𝟘 ≤ω 𝟘 𝟘 → refl
𝟙 𝟘 ≤ω 𝟘 𝟙 → refl
𝟙 𝟘 ≤ω 𝟘 ≤𝟙 → refl
𝟙 𝟘 ≤ω 𝟘 ≤ω → refl
𝟙 𝟘 ≤ω 𝟙 𝟘 → refl
𝟙 𝟘 ≤ω 𝟙 𝟙 → refl
𝟙 𝟘 ≤ω 𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤ω 𝟙 ≤ω → refl
𝟙 𝟘 ≤ω ≤𝟙 𝟘 → refl
𝟙 𝟘 ≤ω ≤𝟙 𝟙 → refl
𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤ω ≤𝟙 ≤ω → refl
𝟙 𝟘 ≤ω ≤ω 𝟘 → refl
𝟙 𝟘 ≤ω ≤ω 𝟙 → refl
𝟙 𝟘 ≤ω ≤ω ≤𝟙 → refl
𝟙 𝟘 ≤ω ≤ω ≤ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ≤ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ≤ω → refl
𝟙 𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟙 𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟙 𝟙 𝟘 ≤ω 𝟘 → refl
𝟙 𝟙 𝟘 ≤ω 𝟙 → refl
𝟙 𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟙 𝟙 𝟘 ≤ω ≤ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ≤ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ≤ω → refl
𝟙 𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟙 𝟙 ≤ω 𝟘 → refl
𝟙 𝟙 𝟙 ≤ω 𝟙 → refl
𝟙 𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟙 𝟙 ≤ω ≤ω → refl
𝟙 𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟙 𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟙 𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟙 𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟙 𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟙 𝟙 ≤ω 𝟘 𝟘 → refl
𝟙 𝟙 ≤ω 𝟘 𝟙 → refl
𝟙 𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟙 𝟙 ≤ω 𝟘 ≤ω → refl
𝟙 𝟙 ≤ω 𝟙 𝟘 → refl
𝟙 𝟙 ≤ω 𝟙 𝟙 → refl
𝟙 𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤ω 𝟙 ≤ω → refl
𝟙 𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟙 𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟙 𝟙 ≤ω ≤ω 𝟘 → refl
𝟙 𝟙 ≤ω ≤ω 𝟙 → refl
𝟙 𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟙 𝟙 ≤ω ≤ω ≤ω → refl
𝟙 ≤𝟙 𝟘 𝟘 𝟘 → refl
𝟙 ≤𝟙 𝟘 𝟘 𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟘 ≤ω → refl
𝟙 ≤𝟙 𝟘 𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟘 𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟘 ≤ω 𝟘 → refl
𝟙 ≤𝟙 𝟘 ≤ω 𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤ω ≤ω → refl
𝟙 ≤𝟙 𝟙 𝟘 𝟘 → refl
𝟙 ≤𝟙 𝟙 𝟘 𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟘 ≤ω → refl
𝟙 ≤𝟙 𝟙 𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟙 𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟙 ≤ω 𝟘 → refl
𝟙 ≤𝟙 𝟙 ≤ω 𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤ω ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟙 ≤𝟙 ≤ω 𝟘 𝟘 → refl
𝟙 ≤𝟙 ≤ω 𝟘 𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟘 ≤ω → refl
𝟙 ≤𝟙 ≤ω 𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤ω 𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤ω ≤ω 𝟘 → refl
𝟙 ≤𝟙 ≤ω ≤ω 𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤ω ≤ω → refl
𝟙 ≤ω 𝟘 𝟘 𝟘 → refl
𝟙 ≤ω 𝟘 𝟘 𝟙 → refl
𝟙 ≤ω 𝟘 𝟘 ≤𝟙 → refl
𝟙 ≤ω 𝟘 𝟘 ≤ω → refl
𝟙 ≤ω 𝟘 𝟙 𝟘 → refl
𝟙 ≤ω 𝟘 𝟙 𝟙 → refl
𝟙 ≤ω 𝟘 𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟘 𝟙 ≤ω → refl
𝟙 ≤ω 𝟘 ≤𝟙 𝟘 → refl
𝟙 ≤ω 𝟘 ≤𝟙 𝟙 → refl
𝟙 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟘 ≤𝟙 ≤ω → refl
𝟙 ≤ω 𝟘 ≤ω 𝟘 → refl
𝟙 ≤ω 𝟘 ≤ω 𝟙 → refl
𝟙 ≤ω 𝟘 ≤ω ≤𝟙 → refl
𝟙 ≤ω 𝟘 ≤ω ≤ω → refl
𝟙 ≤ω 𝟙 𝟘 𝟘 → refl
𝟙 ≤ω 𝟙 𝟘 𝟙 → refl
𝟙 ≤ω 𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤ω 𝟙 𝟘 ≤ω → refl
𝟙 ≤ω 𝟙 𝟙 𝟘 → refl
𝟙 ≤ω 𝟙 𝟙 𝟙 → refl
𝟙 ≤ω 𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟙 𝟙 ≤ω → refl
𝟙 ≤ω 𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤ω 𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤ω 𝟙 ≤ω 𝟘 → refl
𝟙 ≤ω 𝟙 ≤ω 𝟙 → refl
𝟙 ≤ω 𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤ω 𝟙 ≤ω ≤ω → refl
𝟙 ≤ω ≤𝟙 𝟘 𝟘 → refl
𝟙 ≤ω ≤𝟙 𝟘 𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟘 ≤ω → refl
𝟙 ≤ω ≤𝟙 𝟙 𝟘 → refl
𝟙 ≤ω ≤𝟙 𝟙 𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟙 ≤ω → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤ω ≤𝟙 ≤ω 𝟘 → refl
𝟙 ≤ω ≤𝟙 ≤ω 𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤ω ≤ω → refl
𝟙 ≤ω ≤ω 𝟘 𝟘 → refl
𝟙 ≤ω ≤ω 𝟘 𝟙 → refl
𝟙 ≤ω ≤ω 𝟘 ≤𝟙 → refl
𝟙 ≤ω ≤ω 𝟘 ≤ω → refl
𝟙 ≤ω ≤ω 𝟙 𝟘 → refl
𝟙 ≤ω ≤ω 𝟙 𝟙 → refl
𝟙 ≤ω ≤ω 𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤ω 𝟙 ≤ω → refl
𝟙 ≤ω ≤ω ≤𝟙 𝟘 → refl
𝟙 ≤ω ≤ω ≤𝟙 𝟙 → refl
𝟙 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤ω ≤𝟙 ≤ω → refl
𝟙 ≤ω ≤ω ≤ω 𝟘 → refl
𝟙 ≤ω ≤ω ≤ω 𝟙 → refl
𝟙 ≤ω ≤ω ≤ω ≤𝟙 → refl
𝟙 ≤ω ≤ω ≤ω ≤ω → refl
≤𝟙 𝟘 𝟘 𝟘 𝟘 → refl
≤𝟙 𝟘 𝟘 𝟘 𝟙 → refl
≤𝟙 𝟘 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 𝟘 ≤ω → refl
≤𝟙 𝟘 𝟘 𝟙 𝟘 → refl
≤𝟙 𝟘 𝟘 𝟙 𝟙 → refl
≤𝟙 𝟘 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 𝟙 ≤ω → refl
≤𝟙 𝟘 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 𝟘 ≤ω 𝟘 → refl
≤𝟙 𝟘 𝟘 ≤ω 𝟙 → refl
≤𝟙 𝟘 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 𝟘 ≤ω ≤ω → refl
≤𝟙 𝟘 𝟙 𝟘 𝟘 → refl
≤𝟙 𝟘 𝟙 𝟘 𝟙 → refl
≤𝟙 𝟘 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 𝟘 ≤ω → refl
≤𝟙 𝟘 𝟙 𝟙 𝟘 → refl
≤𝟙 𝟘 𝟙 𝟙 𝟙 → refl
≤𝟙 𝟘 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 𝟙 ≤ω → refl
≤𝟙 𝟘 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟘 𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟘 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 𝟙 ≤ω ≤ω → refl
≤𝟙 𝟘 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 𝟘 ≤ω 𝟘 𝟘 → refl
≤𝟙 𝟘 ≤ω 𝟘 𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟘 ≤ω → refl
≤𝟙 𝟘 ≤ω 𝟙 𝟘 → refl
≤𝟙 𝟘 ≤ω 𝟙 𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟙 ≤ω → refl
≤𝟙 𝟘 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 𝟘 ≤ω ≤ω 𝟘 → refl
≤𝟙 𝟘 ≤ω ≤ω 𝟙 → refl
≤𝟙 𝟘 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 𝟘 ≤ω ≤ω ≤ω → refl
≤𝟙 𝟙 𝟘 𝟘 𝟘 → refl
≤𝟙 𝟙 𝟘 𝟘 𝟙 → refl
≤𝟙 𝟙 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 𝟘 ≤ω → refl
≤𝟙 𝟙 𝟘 𝟙 𝟘 → refl
≤𝟙 𝟙 𝟘 𝟙 𝟙 → refl
≤𝟙 𝟙 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 𝟙 ≤ω → refl
≤𝟙 𝟙 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 𝟘 ≤ω 𝟘 → refl
≤𝟙 𝟙 𝟘 ≤ω 𝟙 → refl
≤𝟙 𝟙 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 𝟘 ≤ω ≤ω → refl
≤𝟙 𝟙 𝟙 𝟘 𝟘 → refl
≤𝟙 𝟙 𝟙 𝟘 𝟙 → refl
≤𝟙 𝟙 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 𝟘 ≤ω → refl
≤𝟙 𝟙 𝟙 𝟙 𝟘 → refl
≤𝟙 𝟙 𝟙 𝟙 𝟙 → refl
≤𝟙 𝟙 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 𝟙 ≤ω → refl
≤𝟙 𝟙 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟙 𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟙 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 𝟙 ≤ω ≤ω → refl
≤𝟙 𝟙 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 𝟙 ≤ω 𝟘 𝟘 → refl
≤𝟙 𝟙 ≤ω 𝟘 𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟘 ≤ω → refl
≤𝟙 𝟙 ≤ω 𝟙 𝟘 → refl
≤𝟙 𝟙 ≤ω 𝟙 𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟙 ≤ω → refl
≤𝟙 𝟙 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 𝟙 ≤ω ≤ω 𝟘 → refl
≤𝟙 𝟙 ≤ω ≤ω 𝟙 → refl
≤𝟙 𝟙 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 𝟙 ≤ω ≤ω ≤ω → refl
≤𝟙 ≤𝟙 𝟘 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 𝟙 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω ≤ω → refl
≤𝟙 ≤ω 𝟘 𝟘 𝟘 → refl
≤𝟙 ≤ω 𝟘 𝟘 𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟘 ≤ω → refl
≤𝟙 ≤ω 𝟘 𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟘 𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟘 ≤ω 𝟘 → refl
≤𝟙 ≤ω 𝟘 ≤ω 𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤ω ≤ω → refl
≤𝟙 ≤ω 𝟙 𝟘 𝟘 → refl
≤𝟙 ≤ω 𝟙 𝟘 𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟘 ≤ω → refl
≤𝟙 ≤ω 𝟙 𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟙 𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤ω 𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤ω ≤ω → refl
≤𝟙 ≤ω ≤𝟙 𝟘 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 𝟙 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω ≤ω → refl
≤𝟙 ≤ω ≤ω 𝟘 𝟘 → refl
≤𝟙 ≤ω ≤ω 𝟘 𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟘 ≤ω → refl
≤𝟙 ≤ω ≤ω 𝟙 𝟘 → refl
≤𝟙 ≤ω ≤ω 𝟙 𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟙 ≤ω → refl
≤𝟙 ≤ω ≤ω ≤𝟙 𝟘 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 𝟙 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 ≤ω → refl
≤𝟙 ≤ω ≤ω ≤ω 𝟘 → refl
≤𝟙 ≤ω ≤ω ≤ω 𝟙 → refl
≤𝟙 ≤ω ≤ω ≤ω ≤𝟙 → refl
≤𝟙 ≤ω ≤ω ≤ω ≤ω → refl
≤ω 𝟘 𝟘 𝟘 𝟘 → refl
≤ω 𝟘 𝟘 𝟘 𝟙 → refl
≤ω 𝟘 𝟘 𝟘 ≤𝟙 → refl
≤ω 𝟘 𝟘 𝟘 ≤ω → refl
≤ω 𝟘 𝟘 𝟙 𝟘 → refl
≤ω 𝟘 𝟘 𝟙 𝟙 → refl
≤ω 𝟘 𝟘 𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟘 𝟙 ≤ω → refl
≤ω 𝟘 𝟘 ≤𝟙 𝟘 → refl
≤ω 𝟘 𝟘 ≤𝟙 𝟙 → refl
≤ω 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟘 ≤𝟙 ≤ω → refl
≤ω 𝟘 𝟘 ≤ω 𝟘 → refl
≤ω 𝟘 𝟘 ≤ω 𝟙 → refl
≤ω 𝟘 𝟘 ≤ω ≤𝟙 → refl
≤ω 𝟘 𝟘 ≤ω ≤ω → refl
≤ω 𝟘 𝟙 𝟘 𝟘 → refl
≤ω 𝟘 𝟙 𝟘 𝟙 → refl
≤ω 𝟘 𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟘 𝟙 𝟘 ≤ω → refl
≤ω 𝟘 𝟙 𝟙 𝟘 → refl
≤ω 𝟘 𝟙 𝟙 𝟙 → refl
≤ω 𝟘 𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟙 𝟙 ≤ω → refl
≤ω 𝟘 𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟘 𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟘 𝟙 ≤ω 𝟘 → refl
≤ω 𝟘 𝟙 ≤ω 𝟙 → refl
≤ω 𝟘 𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟘 𝟙 ≤ω ≤ω → refl
≤ω 𝟘 ≤𝟙 𝟘 𝟘 → refl
≤ω 𝟘 ≤𝟙 𝟘 𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟘 ≤ω → refl
≤ω 𝟘 ≤𝟙 𝟙 𝟘 → refl
≤ω 𝟘 ≤𝟙 𝟙 𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟙 ≤ω → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟘 ≤𝟙 ≤ω 𝟘 → refl
≤ω 𝟘 ≤𝟙 ≤ω 𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤ω ≤ω → refl
≤ω 𝟘 ≤ω 𝟘 𝟘 → refl
≤ω 𝟘 ≤ω 𝟘 𝟙 → refl
≤ω 𝟘 ≤ω 𝟘 ≤𝟙 → refl
≤ω 𝟘 ≤ω 𝟘 ≤ω → refl
≤ω 𝟘 ≤ω 𝟙 𝟘 → refl
≤ω 𝟘 ≤ω 𝟙 𝟙 → refl
≤ω 𝟘 ≤ω 𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤ω 𝟙 ≤ω → refl
≤ω 𝟘 ≤ω ≤𝟙 𝟘 → refl
≤ω 𝟘 ≤ω ≤𝟙 𝟙 → refl
≤ω 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤ω ≤𝟙 ≤ω → refl
≤ω 𝟘 ≤ω ≤ω 𝟘 → refl
≤ω 𝟘 ≤ω ≤ω 𝟙 → refl
≤ω 𝟘 ≤ω ≤ω ≤𝟙 → refl
≤ω 𝟘 ≤ω ≤ω ≤ω → refl
≤ω 𝟙 𝟘 𝟘 𝟘 → refl
≤ω 𝟙 𝟘 𝟘 𝟙 → refl
≤ω 𝟙 𝟘 𝟘 ≤𝟙 → refl
≤ω 𝟙 𝟘 𝟘 ≤ω → refl
≤ω 𝟙 𝟘 𝟙 𝟘 → refl
≤ω 𝟙 𝟘 𝟙 𝟙 → refl
≤ω 𝟙 𝟘 𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟘 𝟙 ≤ω → refl
≤ω 𝟙 𝟘 ≤𝟙 𝟘 → refl
≤ω 𝟙 𝟘 ≤𝟙 𝟙 → refl
≤ω 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟘 ≤𝟙 ≤ω → refl
≤ω 𝟙 𝟘 ≤ω 𝟘 → refl
≤ω 𝟙 𝟘 ≤ω 𝟙 → refl
≤ω 𝟙 𝟘 ≤ω ≤𝟙 → refl
≤ω 𝟙 𝟘 ≤ω ≤ω → refl
≤ω 𝟙 𝟙 𝟘 𝟘 → refl
≤ω 𝟙 𝟙 𝟘 𝟙 → refl
≤ω 𝟙 𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟙 𝟙 𝟘 ≤ω → refl
≤ω 𝟙 𝟙 𝟙 𝟘 → refl
≤ω 𝟙 𝟙 𝟙 𝟙 → refl
≤ω 𝟙 𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟙 𝟙 ≤ω → refl
≤ω 𝟙 𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟙 𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟙 𝟙 ≤ω 𝟘 → refl
≤ω 𝟙 𝟙 ≤ω 𝟙 → refl
≤ω 𝟙 𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟙 𝟙 ≤ω ≤ω → refl
≤ω 𝟙 ≤𝟙 𝟘 𝟘 → refl
≤ω 𝟙 ≤𝟙 𝟘 𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟘 ≤ω → refl
≤ω 𝟙 ≤𝟙 𝟙 𝟘 → refl
≤ω 𝟙 ≤𝟙 𝟙 𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟙 ≤ω → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤ω 𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤ω ≤ω → refl
≤ω 𝟙 ≤ω 𝟘 𝟘 → refl
≤ω 𝟙 ≤ω 𝟘 𝟙 → refl
≤ω 𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤ω 𝟙 ≤ω 𝟘 ≤ω → refl
≤ω 𝟙 ≤ω 𝟙 𝟘 → refl
≤ω 𝟙 ≤ω 𝟙 𝟙 → refl
≤ω 𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤ω 𝟙 ≤ω → refl
≤ω 𝟙 ≤ω ≤𝟙 𝟘 → refl
≤ω 𝟙 ≤ω ≤𝟙 𝟙 → refl
≤ω 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤ω ≤𝟙 ≤ω → refl
≤ω 𝟙 ≤ω ≤ω 𝟘 → refl
≤ω 𝟙 ≤ω ≤ω 𝟙 → refl
≤ω 𝟙 ≤ω ≤ω ≤𝟙 → refl
≤ω 𝟙 ≤ω ≤ω ≤ω → refl
≤ω ≤𝟙 𝟘 𝟘 𝟘 → refl
≤ω ≤𝟙 𝟘 𝟘 𝟙 → refl
≤ω ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 𝟘 ≤ω → refl
≤ω ≤𝟙 𝟘 𝟙 𝟘 → refl
≤ω ≤𝟙 𝟘 𝟙 𝟙 → refl
≤ω ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 𝟙 ≤ω → refl
≤ω ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 𝟘 ≤ω 𝟘 → refl
≤ω ≤𝟙 𝟘 ≤ω 𝟙 → refl
≤ω ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 𝟘 ≤ω ≤ω → refl
≤ω ≤𝟙 𝟙 𝟘 𝟘 → refl
≤ω ≤𝟙 𝟙 𝟘 𝟙 → refl
≤ω ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 𝟘 ≤ω → refl
≤ω ≤𝟙 𝟙 𝟙 𝟘 → refl
≤ω ≤𝟙 𝟙 𝟙 𝟙 → refl
≤ω ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 𝟙 ≤ω → refl
≤ω ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 𝟙 ≤ω 𝟘 → refl
≤ω ≤𝟙 𝟙 ≤ω 𝟙 → refl
≤ω ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 𝟙 ≤ω ≤ω → refl
≤ω ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
≤ω ≤𝟙 ≤ω 𝟘 𝟘 → refl
≤ω ≤𝟙 ≤ω 𝟘 𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟘 ≤ω → refl
≤ω ≤𝟙 ≤ω 𝟙 𝟘 → refl
≤ω ≤𝟙 ≤ω 𝟙 𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟙 ≤ω → refl
≤ω ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
≤ω ≤𝟙 ≤ω ≤ω 𝟘 → refl
≤ω ≤𝟙 ≤ω ≤ω 𝟙 → refl
≤ω ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
≤ω ≤𝟙 ≤ω ≤ω ≤ω → refl
≤ω ≤ω 𝟘 𝟘 𝟘 → refl
≤ω ≤ω 𝟘 𝟘 𝟙 → refl
≤ω ≤ω 𝟘 𝟘 ≤𝟙 → refl
≤ω ≤ω 𝟘 𝟘 ≤ω → refl
≤ω ≤ω 𝟘 𝟙 𝟘 → refl
≤ω ≤ω 𝟘 𝟙 𝟙 → refl
≤ω ≤ω 𝟘 𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟘 𝟙 ≤ω → refl
≤ω ≤ω 𝟘 ≤𝟙 𝟘 → refl
≤ω ≤ω 𝟘 ≤𝟙 𝟙 → refl
≤ω ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟘 ≤𝟙 ≤ω → refl
≤ω ≤ω 𝟘 ≤ω 𝟘 → refl
≤ω ≤ω 𝟘 ≤ω 𝟙 → refl
≤ω ≤ω 𝟘 ≤ω ≤𝟙 → refl
≤ω ≤ω 𝟘 ≤ω ≤ω → refl
≤ω ≤ω 𝟙 𝟘 𝟘 → refl
≤ω ≤ω 𝟙 𝟘 𝟙 → refl
≤ω ≤ω 𝟙 𝟘 ≤𝟙 → refl
≤ω ≤ω 𝟙 𝟘 ≤ω → refl
≤ω ≤ω 𝟙 𝟙 𝟘 → refl
≤ω ≤ω 𝟙 𝟙 𝟙 → refl
≤ω ≤ω 𝟙 𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟙 𝟙 ≤ω → refl
≤ω ≤ω 𝟙 ≤𝟙 𝟘 → refl
≤ω ≤ω 𝟙 ≤𝟙 𝟙 → refl
≤ω ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟙 ≤𝟙 ≤ω → refl
≤ω ≤ω 𝟙 ≤ω 𝟘 → refl
≤ω ≤ω 𝟙 ≤ω 𝟙 → refl
≤ω ≤ω 𝟙 ≤ω ≤𝟙 → refl
≤ω ≤ω 𝟙 ≤ω ≤ω → refl
≤ω ≤ω ≤𝟙 𝟘 𝟘 → refl
≤ω ≤ω ≤𝟙 𝟘 𝟙 → refl
≤ω ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 𝟘 ≤ω → refl
≤ω ≤ω ≤𝟙 𝟙 𝟘 → refl
≤ω ≤ω ≤𝟙 𝟙 𝟙 → refl
≤ω ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 𝟙 ≤ω → refl
≤ω ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
≤ω ≤ω ≤𝟙 ≤ω 𝟘 → refl
≤ω ≤ω ≤𝟙 ≤ω 𝟙 → refl
≤ω ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
≤ω ≤ω ≤𝟙 ≤ω ≤ω → refl
≤ω ≤ω ≤ω 𝟘 𝟘 → refl
≤ω ≤ω ≤ω 𝟘 𝟙 → refl
≤ω ≤ω ≤ω 𝟘 ≤𝟙 → refl
≤ω ≤ω ≤ω 𝟘 ≤ω → refl
≤ω ≤ω ≤ω 𝟙 𝟘 → refl
≤ω ≤ω ≤ω 𝟙 𝟙 → refl
≤ω ≤ω ≤ω 𝟙 ≤𝟙 → refl
≤ω ≤ω ≤ω 𝟙 ≤ω → refl
≤ω ≤ω ≤ω ≤𝟙 𝟘 → refl
≤ω ≤ω ≤ω ≤𝟙 𝟙 → refl
≤ω ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
≤ω ≤ω ≤ω ≤𝟙 ≤ω → refl
≤ω ≤ω ≤ω ≤ω 𝟘 → refl
≤ω ≤ω ≤ω ≤ω 𝟙 → refl
≤ω ≤ω ≤ω ≤ω ≤𝟙 → refl
≤ω ≤ω ≤ω ≤ω ≤ω → refl
opaque
linear-or-affine⇨linearity-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(linear-or-affine v₁)
(linearityModality v₂)
linear-or-affine→linearity
linear-or-affine⇨linearity-no-nr-preserving {v₁ = record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ LA.linear-or-affine-has-well-behaved-zero
where
open Is-no-nr-preserving-morphism
opaque
linear-or-affine⇨linearity-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(linear-or-affine v₁)
(linearityModality v₂)
linear-or-affine→linearity
linear-or-affine⇨linearity-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , L.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , L.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
affine⇨linear-or-affine-nr-preserving :
Is-nr-preserving-morphism
(affineModality v₁)
(linear-or-affine v₂)
⦃ A.zero-one-many-has-nr ⦄
⦃ LA.linear-or-affine-has-nr ⦄
affine→linear-or-affine
affine⇨linear-or-affine-nr-preserving {v₂} = λ where
.tr-nr {r} → ≤-reflexive (tr-nr′ _ r _ _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (linear-or-affine v₂)
tr : Affine → Linear-or-affine
tr = affine→linear-or-affine
tr-nr′ :
∀ p r z s n →
tr (A.nr p r z s n) ≡
LA.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ω → refl
𝟘 𝟘 𝟘 ω 𝟘 → refl
𝟘 𝟘 𝟘 ω 𝟙 → refl
𝟘 𝟘 𝟘 ω ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ω → refl
𝟘 𝟘 𝟙 ω 𝟘 → refl
𝟘 𝟘 𝟙 ω 𝟙 → refl
𝟘 𝟘 𝟙 ω ω → refl
𝟘 𝟘 ω 𝟘 𝟘 → refl
𝟘 𝟘 ω 𝟘 𝟙 → refl
𝟘 𝟘 ω 𝟘 ω → refl
𝟘 𝟘 ω 𝟙 𝟘 → refl
𝟘 𝟘 ω 𝟙 𝟙 → refl
𝟘 𝟘 ω 𝟙 ω → refl
𝟘 𝟘 ω ω 𝟘 → refl
𝟘 𝟘 ω ω 𝟙 → refl
𝟘 𝟘 ω ω ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ω → refl
𝟘 𝟙 𝟘 ω 𝟘 → refl
𝟘 𝟙 𝟘 ω 𝟙 → refl
𝟘 𝟙 𝟘 ω ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ω → refl
𝟘 𝟙 𝟙 ω 𝟘 → refl
𝟘 𝟙 𝟙 ω 𝟙 → refl
𝟘 𝟙 𝟙 ω ω → refl
𝟘 𝟙 ω 𝟘 𝟘 → refl
𝟘 𝟙 ω 𝟘 𝟙 → refl
𝟘 𝟙 ω 𝟘 ω → refl
𝟘 𝟙 ω 𝟙 𝟘 → refl
𝟘 𝟙 ω 𝟙 𝟙 → refl
𝟘 𝟙 ω 𝟙 ω → refl
𝟘 𝟙 ω ω 𝟘 → refl
𝟘 𝟙 ω ω 𝟙 → refl
𝟘 𝟙 ω ω ω → refl
𝟘 ω 𝟘 𝟘 𝟘 → refl
𝟘 ω 𝟘 𝟘 𝟙 → refl
𝟘 ω 𝟘 𝟘 ω → refl
𝟘 ω 𝟘 𝟙 𝟘 → refl
𝟘 ω 𝟘 𝟙 𝟙 → refl
𝟘 ω 𝟘 𝟙 ω → refl
𝟘 ω 𝟘 ω 𝟘 → refl
𝟘 ω 𝟘 ω 𝟙 → refl
𝟘 ω 𝟘 ω ω → refl
𝟘 ω 𝟙 𝟘 𝟘 → refl
𝟘 ω 𝟙 𝟘 𝟙 → refl
𝟘 ω 𝟙 𝟘 ω → refl
𝟘 ω 𝟙 𝟙 𝟘 → refl
𝟘 ω 𝟙 𝟙 𝟙 → refl
𝟘 ω 𝟙 𝟙 ω → refl
𝟘 ω 𝟙 ω 𝟘 → refl
𝟘 ω 𝟙 ω 𝟙 → refl
𝟘 ω 𝟙 ω ω → refl
𝟘 ω ω 𝟘 𝟘 → refl
𝟘 ω ω 𝟘 𝟙 → refl
𝟘 ω ω 𝟘 ω → refl
𝟘 ω ω 𝟙 𝟘 → refl
𝟘 ω ω 𝟙 𝟙 → refl
𝟘 ω ω 𝟙 ω → refl
𝟘 ω ω ω 𝟘 → refl
𝟘 ω ω ω 𝟙 → refl
𝟘 ω ω ω ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ω → refl
𝟙 𝟘 𝟘 ω 𝟘 → refl
𝟙 𝟘 𝟘 ω 𝟙 → refl
𝟙 𝟘 𝟘 ω ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ω → refl
𝟙 𝟘 𝟙 ω 𝟘 → refl
𝟙 𝟘 𝟙 ω 𝟙 → refl
𝟙 𝟘 𝟙 ω ω → refl
𝟙 𝟘 ω 𝟘 𝟘 → refl
𝟙 𝟘 ω 𝟘 𝟙 → refl
𝟙 𝟘 ω 𝟘 ω → refl
𝟙 𝟘 ω 𝟙 𝟘 → refl
𝟙 𝟘 ω 𝟙 𝟙 → refl
𝟙 𝟘 ω 𝟙 ω → refl
𝟙 𝟘 ω ω 𝟘 → refl
𝟙 𝟘 ω ω 𝟙 → refl
𝟙 𝟘 ω ω ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ω → refl
𝟙 𝟙 𝟘 ω 𝟘 → refl
𝟙 𝟙 𝟘 ω 𝟙 → refl
𝟙 𝟙 𝟘 ω ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ω → refl
𝟙 𝟙 𝟙 ω 𝟘 → refl
𝟙 𝟙 𝟙 ω 𝟙 → refl
𝟙 𝟙 𝟙 ω ω → refl
𝟙 𝟙 ω 𝟘 𝟘 → refl
𝟙 𝟙 ω 𝟘 𝟙 → refl
𝟙 𝟙 ω 𝟘 ω → refl
𝟙 𝟙 ω 𝟙 𝟘 → refl
𝟙 𝟙 ω 𝟙 𝟙 → refl
𝟙 𝟙 ω 𝟙 ω → refl
𝟙 𝟙 ω ω 𝟘 → refl
𝟙 𝟙 ω ω 𝟙 → refl
𝟙 𝟙 ω ω ω → refl
𝟙 ω 𝟘 𝟘 𝟘 → refl
𝟙 ω 𝟘 𝟘 𝟙 → refl
𝟙 ω 𝟘 𝟘 ω → refl
𝟙 ω 𝟘 𝟙 𝟘 → refl
𝟙 ω 𝟘 𝟙 𝟙 → refl
𝟙 ω 𝟘 𝟙 ω → refl
𝟙 ω 𝟘 ω 𝟘 → refl
𝟙 ω 𝟘 ω 𝟙 → refl
𝟙 ω 𝟘 ω ω → refl
𝟙 ω 𝟙 𝟘 𝟘 → refl
𝟙 ω 𝟙 𝟘 𝟙 → refl
𝟙 ω 𝟙 𝟘 ω → refl
𝟙 ω 𝟙 𝟙 𝟘 → refl
𝟙 ω 𝟙 𝟙 𝟙 → refl
𝟙 ω 𝟙 𝟙 ω → refl
𝟙 ω 𝟙 ω 𝟘 → refl
𝟙 ω 𝟙 ω 𝟙 → refl
𝟙 ω 𝟙 ω ω → refl
𝟙 ω ω 𝟘 𝟘 → refl
𝟙 ω ω 𝟘 𝟙 → refl
𝟙 ω ω 𝟘 ω → refl
𝟙 ω ω 𝟙 𝟘 → refl
𝟙 ω ω 𝟙 𝟙 → refl
𝟙 ω ω 𝟙 ω → refl
𝟙 ω ω ω 𝟘 → refl
𝟙 ω ω ω 𝟙 → refl
𝟙 ω ω ω ω → refl
ω 𝟘 𝟘 𝟘 𝟘 → refl
ω 𝟘 𝟘 𝟘 𝟙 → refl
ω 𝟘 𝟘 𝟘 ω → refl
ω 𝟘 𝟘 𝟙 𝟘 → refl
ω 𝟘 𝟘 𝟙 𝟙 → refl
ω 𝟘 𝟘 𝟙 ω → refl
ω 𝟘 𝟘 ω 𝟘 → refl
ω 𝟘 𝟘 ω 𝟙 → refl
ω 𝟘 𝟘 ω ω → refl
ω 𝟘 𝟙 𝟘 𝟘 → refl
ω 𝟘 𝟙 𝟘 𝟙 → refl
ω 𝟘 𝟙 𝟘 ω → refl
ω 𝟘 𝟙 𝟙 𝟘 → refl
ω 𝟘 𝟙 𝟙 𝟙 → refl
ω 𝟘 𝟙 𝟙 ω → refl
ω 𝟘 𝟙 ω 𝟘 → refl
ω 𝟘 𝟙 ω 𝟙 → refl
ω 𝟘 𝟙 ω ω → refl
ω 𝟘 ω 𝟘 𝟘 → refl
ω 𝟘 ω 𝟘 𝟙 → refl
ω 𝟘 ω 𝟘 ω → refl
ω 𝟘 ω 𝟙 𝟘 → refl
ω 𝟘 ω 𝟙 𝟙 → refl
ω 𝟘 ω 𝟙 ω → refl
ω 𝟘 ω ω 𝟘 → refl
ω 𝟘 ω ω 𝟙 → refl
ω 𝟘 ω ω ω → refl
ω 𝟙 𝟘 𝟘 𝟘 → refl
ω 𝟙 𝟘 𝟘 𝟙 → refl
ω 𝟙 𝟘 𝟘 ω → refl
ω 𝟙 𝟘 𝟙 𝟘 → refl
ω 𝟙 𝟘 𝟙 𝟙 → refl
ω 𝟙 𝟘 𝟙 ω → refl
ω 𝟙 𝟘 ω 𝟘 → refl
ω 𝟙 𝟘 ω 𝟙 → refl
ω 𝟙 𝟘 ω ω → refl
ω 𝟙 𝟙 𝟘 𝟘 → refl
ω 𝟙 𝟙 𝟘 𝟙 → refl
ω 𝟙 𝟙 𝟘 ω → refl
ω 𝟙 𝟙 𝟙 𝟘 → refl
ω 𝟙 𝟙 𝟙 𝟙 → refl
ω 𝟙 𝟙 𝟙 ω → refl
ω 𝟙 𝟙 ω 𝟘 → refl
ω 𝟙 𝟙 ω 𝟙 → refl
ω 𝟙 𝟙 ω ω → refl
ω 𝟙 ω 𝟘 𝟘 → refl
ω 𝟙 ω 𝟘 𝟙 → refl
ω 𝟙 ω 𝟘 ω → refl
ω 𝟙 ω 𝟙 𝟘 → refl
ω 𝟙 ω 𝟙 𝟙 → refl
ω 𝟙 ω 𝟙 ω → refl
ω 𝟙 ω ω 𝟘 → refl
ω 𝟙 ω ω 𝟙 → refl
ω 𝟙 ω ω ω → refl
ω ω 𝟘 𝟘 𝟘 → refl
ω ω 𝟘 𝟘 𝟙 → refl
ω ω 𝟘 𝟘 ω → refl
ω ω 𝟘 𝟙 𝟘 → refl
ω ω 𝟘 𝟙 𝟙 → refl
ω ω 𝟘 𝟙 ω → refl
ω ω 𝟘 ω 𝟘 → refl
ω ω 𝟘 ω 𝟙 → refl
ω ω 𝟘 ω ω → refl
ω ω 𝟙 𝟘 𝟘 → refl
ω ω 𝟙 𝟘 𝟙 → refl
ω ω 𝟙 𝟘 ω → refl
ω ω 𝟙 𝟙 𝟘 → refl
ω ω 𝟙 𝟙 𝟙 → refl
ω ω 𝟙 𝟙 ω → refl
ω ω 𝟙 ω 𝟘 → refl
ω ω 𝟙 ω 𝟙 → refl
ω ω 𝟙 ω ω → refl
ω ω ω 𝟘 𝟘 → refl
ω ω ω 𝟘 𝟙 → refl
ω ω ω 𝟘 ω → refl
ω ω ω 𝟙 𝟘 → refl
ω ω ω 𝟙 𝟙 → refl
ω ω ω 𝟙 ω → refl
ω ω ω ω 𝟘 → refl
ω ω ω ω 𝟙 → refl
ω ω ω ω ω → refl
opaque
affine⇨linear-or-affine-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(affineModality v₁)
(linear-or-affine v₂)
affine→linear-or-affine
affine⇨linear-or-affine-no-nr-preserving {v₁ = v₁@record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ (A.affine-has-well-behaved-zero v₁)
where
open Is-no-nr-preserving-morphism
opaque
affine⇨linear-or-affine-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(affineModality v₁)
(linear-or-affine v₂)
affine→linear-or-affine
affine⇨linear-or-affine-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , LA.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , LA.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
linear-or-affine⇨affine-nr-preserving :
Is-nr-preserving-morphism
(linear-or-affine v₁)
(affineModality v₂)
⦃ LA.linear-or-affine-has-nr ⦄
⦃ A.zero-one-many-has-nr ⦄
linear-or-affine→affine
linear-or-affine⇨affine-nr-preserving {v₂} = λ where
.tr-nr {r} → ≤-reflexive (tr-nr′ _ r _ _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (affineModality v₂)
tr : Linear-or-affine → Affine
tr = linear-or-affine→affine
tr-nr′ :
∀ p r z s n →
tr (LA.nr p r z s n) ≡
A.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ≤𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ≤ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ≤ω → refl
𝟘 𝟘 𝟘 ≤𝟙 𝟘 → refl
𝟘 𝟘 𝟘 ≤𝟙 𝟙 → refl
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟘 ≤𝟙 ≤ω → refl
𝟘 𝟘 𝟘 ≤ω 𝟘 → refl
𝟘 𝟘 𝟘 ≤ω 𝟙 → refl
𝟘 𝟘 𝟘 ≤ω ≤𝟙 → refl
𝟘 𝟘 𝟘 ≤ω ≤ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ≤ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ≤ω → refl
𝟘 𝟘 𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟘 𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟘 𝟙 ≤ω 𝟘 → refl
𝟘 𝟘 𝟙 ≤ω 𝟙 → refl
𝟘 𝟘 𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟘 𝟙 ≤ω ≤ω → refl
𝟘 𝟘 ≤𝟙 𝟘 𝟘 → refl
𝟘 𝟘 ≤𝟙 𝟘 𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟘 ≤ω → refl
𝟘 𝟘 ≤𝟙 𝟙 𝟘 → refl
𝟘 𝟘 ≤𝟙 𝟙 𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 𝟙 ≤ω → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟘 ≤𝟙 ≤ω 𝟘 → refl
𝟘 𝟘 ≤𝟙 ≤ω 𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟘 ≤𝟙 ≤ω ≤ω → refl
𝟘 𝟘 ≤ω 𝟘 𝟘 → refl
𝟘 𝟘 ≤ω 𝟘 𝟙 → refl
𝟘 𝟘 ≤ω 𝟘 ≤𝟙 → refl
𝟘 𝟘 ≤ω 𝟘 ≤ω → refl
𝟘 𝟘 ≤ω 𝟙 𝟘 → refl
𝟘 𝟘 ≤ω 𝟙 𝟙 → refl
𝟘 𝟘 ≤ω 𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤ω 𝟙 ≤ω → refl
𝟘 𝟘 ≤ω ≤𝟙 𝟘 → refl
𝟘 𝟘 ≤ω ≤𝟙 𝟙 → refl
𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 𝟘 ≤ω ≤𝟙 ≤ω → refl
𝟘 𝟘 ≤ω ≤ω 𝟘 → refl
𝟘 𝟘 ≤ω ≤ω 𝟙 → refl
𝟘 𝟘 ≤ω ≤ω ≤𝟙 → refl
𝟘 𝟘 ≤ω ≤ω ≤ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ≤ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ≤ω → refl
𝟘 𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟘 𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟘 𝟙 𝟘 ≤ω 𝟘 → refl
𝟘 𝟙 𝟘 ≤ω 𝟙 → refl
𝟘 𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟘 𝟙 𝟘 ≤ω ≤ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ≤ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ≤ω → refl
𝟘 𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟙 𝟙 ≤ω 𝟘 → refl
𝟘 𝟙 𝟙 ≤ω 𝟙 → refl
𝟘 𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟙 𝟙 ≤ω ≤ω → refl
𝟘 𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟘 𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟘 𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟘 𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟘 𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟘 𝟙 ≤ω 𝟘 𝟘 → refl
𝟘 𝟙 ≤ω 𝟘 𝟙 → refl
𝟘 𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟘 𝟙 ≤ω 𝟘 ≤ω → refl
𝟘 𝟙 ≤ω 𝟙 𝟘 → refl
𝟘 𝟙 ≤ω 𝟙 𝟙 → refl
𝟘 𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤ω 𝟙 ≤ω → refl
𝟘 𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟘 𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟘 𝟙 ≤ω ≤ω 𝟘 → refl
𝟘 𝟙 ≤ω ≤ω 𝟙 → refl
𝟘 𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟘 𝟙 ≤ω ≤ω ≤ω → refl
𝟘 ≤𝟙 𝟘 𝟘 𝟘 → refl
𝟘 ≤𝟙 𝟘 𝟘 𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟘 ≤ω → refl
𝟘 ≤𝟙 𝟘 𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟘 𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟘 ≤ω 𝟘 → refl
𝟘 ≤𝟙 𝟘 ≤ω 𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 𝟘 ≤ω ≤ω → refl
𝟘 ≤𝟙 𝟙 𝟘 𝟘 → refl
𝟘 ≤𝟙 𝟙 𝟘 𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟘 ≤ω → refl
𝟘 ≤𝟙 𝟙 𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟙 𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 𝟙 ≤ω 𝟘 → refl
𝟘 ≤𝟙 𝟙 ≤ω 𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 𝟙 ≤ω ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟘 ≤𝟙 ≤ω 𝟘 𝟘 → refl
𝟘 ≤𝟙 ≤ω 𝟘 𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟘 ≤ω → refl
𝟘 ≤𝟙 ≤ω 𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤ω 𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω 𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟘 ≤𝟙 ≤ω ≤ω 𝟘 → refl
𝟘 ≤𝟙 ≤ω ≤ω 𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟘 ≤𝟙 ≤ω ≤ω ≤ω → refl
𝟘 ≤ω 𝟘 𝟘 𝟘 → refl
𝟘 ≤ω 𝟘 𝟘 𝟙 → refl
𝟘 ≤ω 𝟘 𝟘 ≤𝟙 → refl
𝟘 ≤ω 𝟘 𝟘 ≤ω → refl
𝟘 ≤ω 𝟘 𝟙 𝟘 → refl
𝟘 ≤ω 𝟘 𝟙 𝟙 → refl
𝟘 ≤ω 𝟘 𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟘 𝟙 ≤ω → refl
𝟘 ≤ω 𝟘 ≤𝟙 𝟘 → refl
𝟘 ≤ω 𝟘 ≤𝟙 𝟙 → refl
𝟘 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟘 ≤𝟙 ≤ω → refl
𝟘 ≤ω 𝟘 ≤ω 𝟘 → refl
𝟘 ≤ω 𝟘 ≤ω 𝟙 → refl
𝟘 ≤ω 𝟘 ≤ω ≤𝟙 → refl
𝟘 ≤ω 𝟘 ≤ω ≤ω → refl
𝟘 ≤ω 𝟙 𝟘 𝟘 → refl
𝟘 ≤ω 𝟙 𝟘 𝟙 → refl
𝟘 ≤ω 𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤ω 𝟙 𝟘 ≤ω → refl
𝟘 ≤ω 𝟙 𝟙 𝟘 → refl
𝟘 ≤ω 𝟙 𝟙 𝟙 → refl
𝟘 ≤ω 𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟙 𝟙 ≤ω → refl
𝟘 ≤ω 𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤ω 𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω 𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤ω 𝟙 ≤ω 𝟘 → refl
𝟘 ≤ω 𝟙 ≤ω 𝟙 → refl
𝟘 ≤ω 𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤ω 𝟙 ≤ω ≤ω → refl
𝟘 ≤ω ≤𝟙 𝟘 𝟘 → refl
𝟘 ≤ω ≤𝟙 𝟘 𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟘 ≤ω → refl
𝟘 ≤ω ≤𝟙 𝟙 𝟘 → refl
𝟘 ≤ω ≤𝟙 𝟙 𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 𝟙 ≤ω → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
𝟘 ≤ω ≤𝟙 ≤ω 𝟘 → refl
𝟘 ≤ω ≤𝟙 ≤ω 𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
𝟘 ≤ω ≤𝟙 ≤ω ≤ω → refl
𝟘 ≤ω ≤ω 𝟘 𝟘 → refl
𝟘 ≤ω ≤ω 𝟘 𝟙 → refl
𝟘 ≤ω ≤ω 𝟘 ≤𝟙 → refl
𝟘 ≤ω ≤ω 𝟘 ≤ω → refl
𝟘 ≤ω ≤ω 𝟙 𝟘 → refl
𝟘 ≤ω ≤ω 𝟙 𝟙 → refl
𝟘 ≤ω ≤ω 𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤ω 𝟙 ≤ω → refl
𝟘 ≤ω ≤ω ≤𝟙 𝟘 → refl
𝟘 ≤ω ≤ω ≤𝟙 𝟙 → refl
𝟘 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
𝟘 ≤ω ≤ω ≤𝟙 ≤ω → refl
𝟘 ≤ω ≤ω ≤ω 𝟘 → refl
𝟘 ≤ω ≤ω ≤ω 𝟙 → refl
𝟘 ≤ω ≤ω ≤ω ≤𝟙 → refl
𝟘 ≤ω ≤ω ≤ω ≤ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ≤𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ≤ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ≤ω → refl
𝟙 𝟘 𝟘 ≤𝟙 𝟘 → refl
𝟙 𝟘 𝟘 ≤𝟙 𝟙 → refl
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟘 ≤𝟙 ≤ω → refl
𝟙 𝟘 𝟘 ≤ω 𝟘 → refl
𝟙 𝟘 𝟘 ≤ω 𝟙 → refl
𝟙 𝟘 𝟘 ≤ω ≤𝟙 → refl
𝟙 𝟘 𝟘 ≤ω ≤ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ≤ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ≤ω → refl
𝟙 𝟘 𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟘 𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟘 𝟙 ≤ω 𝟘 → refl
𝟙 𝟘 𝟙 ≤ω 𝟙 → refl
𝟙 𝟘 𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟘 𝟙 ≤ω ≤ω → refl
𝟙 𝟘 ≤𝟙 𝟘 𝟘 → refl
𝟙 𝟘 ≤𝟙 𝟘 𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟘 ≤ω → refl
𝟙 𝟘 ≤𝟙 𝟙 𝟘 → refl
𝟙 𝟘 ≤𝟙 𝟙 𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 𝟙 ≤ω → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟘 ≤𝟙 ≤ω 𝟘 → refl
𝟙 𝟘 ≤𝟙 ≤ω 𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟘 ≤𝟙 ≤ω ≤ω → refl
𝟙 𝟘 ≤ω 𝟘 𝟘 → refl
𝟙 𝟘 ≤ω 𝟘 𝟙 → refl
𝟙 𝟘 ≤ω 𝟘 ≤𝟙 → refl
𝟙 𝟘 ≤ω 𝟘 ≤ω → refl
𝟙 𝟘 ≤ω 𝟙 𝟘 → refl
𝟙 𝟘 ≤ω 𝟙 𝟙 → refl
𝟙 𝟘 ≤ω 𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤ω 𝟙 ≤ω → refl
𝟙 𝟘 ≤ω ≤𝟙 𝟘 → refl
𝟙 𝟘 ≤ω ≤𝟙 𝟙 → refl
𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 𝟘 ≤ω ≤𝟙 ≤ω → refl
𝟙 𝟘 ≤ω ≤ω 𝟘 → refl
𝟙 𝟘 ≤ω ≤ω 𝟙 → refl
𝟙 𝟘 ≤ω ≤ω ≤𝟙 → refl
𝟙 𝟘 ≤ω ≤ω ≤ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ≤ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ≤ω → refl
𝟙 𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟙 𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟙 𝟙 𝟘 ≤ω 𝟘 → refl
𝟙 𝟙 𝟘 ≤ω 𝟙 → refl
𝟙 𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟙 𝟙 𝟘 ≤ω ≤ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ≤ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ≤ω → refl
𝟙 𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟙 𝟙 ≤ω 𝟘 → refl
𝟙 𝟙 𝟙 ≤ω 𝟙 → refl
𝟙 𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟙 𝟙 ≤ω ≤ω → refl
𝟙 𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟙 𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟙 𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟙 𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟙 𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟙 𝟙 ≤ω 𝟘 𝟘 → refl
𝟙 𝟙 ≤ω 𝟘 𝟙 → refl
𝟙 𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟙 𝟙 ≤ω 𝟘 ≤ω → refl
𝟙 𝟙 ≤ω 𝟙 𝟘 → refl
𝟙 𝟙 ≤ω 𝟙 𝟙 → refl
𝟙 𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤ω 𝟙 ≤ω → refl
𝟙 𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟙 𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟙 𝟙 ≤ω ≤ω 𝟘 → refl
𝟙 𝟙 ≤ω ≤ω 𝟙 → refl
𝟙 𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟙 𝟙 ≤ω ≤ω ≤ω → refl
𝟙 ≤𝟙 𝟘 𝟘 𝟘 → refl
𝟙 ≤𝟙 𝟘 𝟘 𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟘 ≤ω → refl
𝟙 ≤𝟙 𝟘 𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟘 𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟘 ≤ω 𝟘 → refl
𝟙 ≤𝟙 𝟘 ≤ω 𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 𝟘 ≤ω ≤ω → refl
𝟙 ≤𝟙 𝟙 𝟘 𝟘 → refl
𝟙 ≤𝟙 𝟙 𝟘 𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟘 ≤ω → refl
𝟙 ≤𝟙 𝟙 𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟙 𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 𝟙 ≤ω 𝟘 → refl
𝟙 ≤𝟙 𝟙 ≤ω 𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 𝟙 ≤ω ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
𝟙 ≤𝟙 ≤ω 𝟘 𝟘 → refl
𝟙 ≤𝟙 ≤ω 𝟘 𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟘 ≤ω → refl
𝟙 ≤𝟙 ≤ω 𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤ω 𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω 𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
𝟙 ≤𝟙 ≤ω ≤ω 𝟘 → refl
𝟙 ≤𝟙 ≤ω ≤ω 𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
𝟙 ≤𝟙 ≤ω ≤ω ≤ω → refl
𝟙 ≤ω 𝟘 𝟘 𝟘 → refl
𝟙 ≤ω 𝟘 𝟘 𝟙 → refl
𝟙 ≤ω 𝟘 𝟘 ≤𝟙 → refl
𝟙 ≤ω 𝟘 𝟘 ≤ω → refl
𝟙 ≤ω 𝟘 𝟙 𝟘 → refl
𝟙 ≤ω 𝟘 𝟙 𝟙 → refl
𝟙 ≤ω 𝟘 𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟘 𝟙 ≤ω → refl
𝟙 ≤ω 𝟘 ≤𝟙 𝟘 → refl
𝟙 ≤ω 𝟘 ≤𝟙 𝟙 → refl
𝟙 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟘 ≤𝟙 ≤ω → refl
𝟙 ≤ω 𝟘 ≤ω 𝟘 → refl
𝟙 ≤ω 𝟘 ≤ω 𝟙 → refl
𝟙 ≤ω 𝟘 ≤ω ≤𝟙 → refl
𝟙 ≤ω 𝟘 ≤ω ≤ω → refl
𝟙 ≤ω 𝟙 𝟘 𝟘 → refl
𝟙 ≤ω 𝟙 𝟘 𝟙 → refl
𝟙 ≤ω 𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤ω 𝟙 𝟘 ≤ω → refl
𝟙 ≤ω 𝟙 𝟙 𝟘 → refl
𝟙 ≤ω 𝟙 𝟙 𝟙 → refl
𝟙 ≤ω 𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟙 𝟙 ≤ω → refl
𝟙 ≤ω 𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤ω 𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω 𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤ω 𝟙 ≤ω 𝟘 → refl
𝟙 ≤ω 𝟙 ≤ω 𝟙 → refl
𝟙 ≤ω 𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤ω 𝟙 ≤ω ≤ω → refl
𝟙 ≤ω ≤𝟙 𝟘 𝟘 → refl
𝟙 ≤ω ≤𝟙 𝟘 𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟘 ≤ω → refl
𝟙 ≤ω ≤𝟙 𝟙 𝟘 → refl
𝟙 ≤ω ≤𝟙 𝟙 𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 𝟙 ≤ω → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
𝟙 ≤ω ≤𝟙 ≤ω 𝟘 → refl
𝟙 ≤ω ≤𝟙 ≤ω 𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
𝟙 ≤ω ≤𝟙 ≤ω ≤ω → refl
𝟙 ≤ω ≤ω 𝟘 𝟘 → refl
𝟙 ≤ω ≤ω 𝟘 𝟙 → refl
𝟙 ≤ω ≤ω 𝟘 ≤𝟙 → refl
𝟙 ≤ω ≤ω 𝟘 ≤ω → refl
𝟙 ≤ω ≤ω 𝟙 𝟘 → refl
𝟙 ≤ω ≤ω 𝟙 𝟙 → refl
𝟙 ≤ω ≤ω 𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤ω 𝟙 ≤ω → refl
𝟙 ≤ω ≤ω ≤𝟙 𝟘 → refl
𝟙 ≤ω ≤ω ≤𝟙 𝟙 → refl
𝟙 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
𝟙 ≤ω ≤ω ≤𝟙 ≤ω → refl
𝟙 ≤ω ≤ω ≤ω 𝟘 → refl
𝟙 ≤ω ≤ω ≤ω 𝟙 → refl
𝟙 ≤ω ≤ω ≤ω ≤𝟙 → refl
𝟙 ≤ω ≤ω ≤ω ≤ω → refl
≤𝟙 𝟘 𝟘 𝟘 𝟘 → refl
≤𝟙 𝟘 𝟘 𝟘 𝟙 → refl
≤𝟙 𝟘 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 𝟘 ≤ω → refl
≤𝟙 𝟘 𝟘 𝟙 𝟘 → refl
≤𝟙 𝟘 𝟘 𝟙 𝟙 → refl
≤𝟙 𝟘 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 𝟙 ≤ω → refl
≤𝟙 𝟘 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 𝟘 ≤ω 𝟘 → refl
≤𝟙 𝟘 𝟘 ≤ω 𝟙 → refl
≤𝟙 𝟘 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 𝟘 ≤ω ≤ω → refl
≤𝟙 𝟘 𝟙 𝟘 𝟘 → refl
≤𝟙 𝟘 𝟙 𝟘 𝟙 → refl
≤𝟙 𝟘 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 𝟘 ≤ω → refl
≤𝟙 𝟘 𝟙 𝟙 𝟘 → refl
≤𝟙 𝟘 𝟙 𝟙 𝟙 → refl
≤𝟙 𝟘 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 𝟙 ≤ω → refl
≤𝟙 𝟘 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟘 𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟘 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 𝟙 ≤ω ≤ω → refl
≤𝟙 𝟘 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟘 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟘 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 𝟘 ≤ω 𝟘 𝟘 → refl
≤𝟙 𝟘 ≤ω 𝟘 𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟘 ≤ω → refl
≤𝟙 𝟘 ≤ω 𝟙 𝟘 → refl
≤𝟙 𝟘 ≤ω 𝟙 𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω 𝟙 ≤ω → refl
≤𝟙 𝟘 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟘 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 𝟘 ≤ω ≤ω 𝟘 → refl
≤𝟙 𝟘 ≤ω ≤ω 𝟙 → refl
≤𝟙 𝟘 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 𝟘 ≤ω ≤ω ≤ω → refl
≤𝟙 𝟙 𝟘 𝟘 𝟘 → refl
≤𝟙 𝟙 𝟘 𝟘 𝟙 → refl
≤𝟙 𝟙 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 𝟘 ≤ω → refl
≤𝟙 𝟙 𝟘 𝟙 𝟘 → refl
≤𝟙 𝟙 𝟘 𝟙 𝟙 → refl
≤𝟙 𝟙 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 𝟙 ≤ω → refl
≤𝟙 𝟙 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 𝟘 ≤ω 𝟘 → refl
≤𝟙 𝟙 𝟘 ≤ω 𝟙 → refl
≤𝟙 𝟙 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 𝟘 ≤ω ≤ω → refl
≤𝟙 𝟙 𝟙 𝟘 𝟘 → refl
≤𝟙 𝟙 𝟙 𝟘 𝟙 → refl
≤𝟙 𝟙 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 𝟘 ≤ω → refl
≤𝟙 𝟙 𝟙 𝟙 𝟘 → refl
≤𝟙 𝟙 𝟙 𝟙 𝟙 → refl
≤𝟙 𝟙 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 𝟙 ≤ω → refl
≤𝟙 𝟙 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟙 𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟙 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 𝟙 ≤ω ≤ω → refl
≤𝟙 𝟙 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 𝟙 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 𝟙 ≤ω 𝟘 𝟘 → refl
≤𝟙 𝟙 ≤ω 𝟘 𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟘 ≤ω → refl
≤𝟙 𝟙 ≤ω 𝟙 𝟘 → refl
≤𝟙 𝟙 ≤ω 𝟙 𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω 𝟙 ≤ω → refl
≤𝟙 𝟙 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 𝟙 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 𝟙 ≤ω ≤ω 𝟘 → refl
≤𝟙 𝟙 ≤ω ≤ω 𝟙 → refl
≤𝟙 𝟙 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 𝟙 ≤ω ≤ω ≤ω → refl
≤𝟙 ≤𝟙 𝟘 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟘 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟘 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 𝟙 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 𝟙 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟘 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω 𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
≤𝟙 ≤𝟙 ≤ω ≤ω 𝟘 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω 𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
≤𝟙 ≤𝟙 ≤ω ≤ω ≤ω → refl
≤𝟙 ≤ω 𝟘 𝟘 𝟘 → refl
≤𝟙 ≤ω 𝟘 𝟘 𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟘 ≤ω → refl
≤𝟙 ≤ω 𝟘 𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟘 𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟘 ≤ω 𝟘 → refl
≤𝟙 ≤ω 𝟘 ≤ω 𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω 𝟘 ≤ω ≤ω → refl
≤𝟙 ≤ω 𝟙 𝟘 𝟘 → refl
≤𝟙 ≤ω 𝟙 𝟘 𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟘 ≤ω → refl
≤𝟙 ≤ω 𝟙 𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟙 𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω 𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤ω 𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω 𝟙 ≤ω ≤ω → refl
≤𝟙 ≤ω ≤𝟙 𝟘 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟘 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 𝟙 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 𝟙 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
≤𝟙 ≤ω ≤𝟙 ≤ω 𝟘 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω 𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
≤𝟙 ≤ω ≤𝟙 ≤ω ≤ω → refl
≤𝟙 ≤ω ≤ω 𝟘 𝟘 → refl
≤𝟙 ≤ω ≤ω 𝟘 𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟘 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟘 ≤ω → refl
≤𝟙 ≤ω ≤ω 𝟙 𝟘 → refl
≤𝟙 ≤ω ≤ω 𝟙 𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω 𝟙 ≤ω → refl
≤𝟙 ≤ω ≤ω ≤𝟙 𝟘 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 𝟙 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω ≤ω ≤𝟙 ≤ω → refl
≤𝟙 ≤ω ≤ω ≤ω 𝟘 → refl
≤𝟙 ≤ω ≤ω ≤ω 𝟙 → refl
≤𝟙 ≤ω ≤ω ≤ω ≤𝟙 → refl
≤𝟙 ≤ω ≤ω ≤ω ≤ω → refl
≤ω 𝟘 𝟘 𝟘 𝟘 → refl
≤ω 𝟘 𝟘 𝟘 𝟙 → refl
≤ω 𝟘 𝟘 𝟘 ≤𝟙 → refl
≤ω 𝟘 𝟘 𝟘 ≤ω → refl
≤ω 𝟘 𝟘 𝟙 𝟘 → refl
≤ω 𝟘 𝟘 𝟙 𝟙 → refl
≤ω 𝟘 𝟘 𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟘 𝟙 ≤ω → refl
≤ω 𝟘 𝟘 ≤𝟙 𝟘 → refl
≤ω 𝟘 𝟘 ≤𝟙 𝟙 → refl
≤ω 𝟘 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟘 ≤𝟙 ≤ω → refl
≤ω 𝟘 𝟘 ≤ω 𝟘 → refl
≤ω 𝟘 𝟘 ≤ω 𝟙 → refl
≤ω 𝟘 𝟘 ≤ω ≤𝟙 → refl
≤ω 𝟘 𝟘 ≤ω ≤ω → refl
≤ω 𝟘 𝟙 𝟘 𝟘 → refl
≤ω 𝟘 𝟙 𝟘 𝟙 → refl
≤ω 𝟘 𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟘 𝟙 𝟘 ≤ω → refl
≤ω 𝟘 𝟙 𝟙 𝟘 → refl
≤ω 𝟘 𝟙 𝟙 𝟙 → refl
≤ω 𝟘 𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟙 𝟙 ≤ω → refl
≤ω 𝟘 𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟘 𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟘 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟘 𝟙 ≤ω 𝟘 → refl
≤ω 𝟘 𝟙 ≤ω 𝟙 → refl
≤ω 𝟘 𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟘 𝟙 ≤ω ≤ω → refl
≤ω 𝟘 ≤𝟙 𝟘 𝟘 → refl
≤ω 𝟘 ≤𝟙 𝟘 𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟘 ≤ω → refl
≤ω 𝟘 ≤𝟙 𝟙 𝟘 → refl
≤ω 𝟘 ≤𝟙 𝟙 𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 𝟙 ≤ω → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟘 ≤𝟙 ≤ω 𝟘 → refl
≤ω 𝟘 ≤𝟙 ≤ω 𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟘 ≤𝟙 ≤ω ≤ω → refl
≤ω 𝟘 ≤ω 𝟘 𝟘 → refl
≤ω 𝟘 ≤ω 𝟘 𝟙 → refl
≤ω 𝟘 ≤ω 𝟘 ≤𝟙 → refl
≤ω 𝟘 ≤ω 𝟘 ≤ω → refl
≤ω 𝟘 ≤ω 𝟙 𝟘 → refl
≤ω 𝟘 ≤ω 𝟙 𝟙 → refl
≤ω 𝟘 ≤ω 𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤ω 𝟙 ≤ω → refl
≤ω 𝟘 ≤ω ≤𝟙 𝟘 → refl
≤ω 𝟘 ≤ω ≤𝟙 𝟙 → refl
≤ω 𝟘 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω 𝟘 ≤ω ≤𝟙 ≤ω → refl
≤ω 𝟘 ≤ω ≤ω 𝟘 → refl
≤ω 𝟘 ≤ω ≤ω 𝟙 → refl
≤ω 𝟘 ≤ω ≤ω ≤𝟙 → refl
≤ω 𝟘 ≤ω ≤ω ≤ω → refl
≤ω 𝟙 𝟘 𝟘 𝟘 → refl
≤ω 𝟙 𝟘 𝟘 𝟙 → refl
≤ω 𝟙 𝟘 𝟘 ≤𝟙 → refl
≤ω 𝟙 𝟘 𝟘 ≤ω → refl
≤ω 𝟙 𝟘 𝟙 𝟘 → refl
≤ω 𝟙 𝟘 𝟙 𝟙 → refl
≤ω 𝟙 𝟘 𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟘 𝟙 ≤ω → refl
≤ω 𝟙 𝟘 ≤𝟙 𝟘 → refl
≤ω 𝟙 𝟘 ≤𝟙 𝟙 → refl
≤ω 𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟘 ≤𝟙 ≤ω → refl
≤ω 𝟙 𝟘 ≤ω 𝟘 → refl
≤ω 𝟙 𝟘 ≤ω 𝟙 → refl
≤ω 𝟙 𝟘 ≤ω ≤𝟙 → refl
≤ω 𝟙 𝟘 ≤ω ≤ω → refl
≤ω 𝟙 𝟙 𝟘 𝟘 → refl
≤ω 𝟙 𝟙 𝟘 𝟙 → refl
≤ω 𝟙 𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟙 𝟙 𝟘 ≤ω → refl
≤ω 𝟙 𝟙 𝟙 𝟘 → refl
≤ω 𝟙 𝟙 𝟙 𝟙 → refl
≤ω 𝟙 𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟙 𝟙 ≤ω → refl
≤ω 𝟙 𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟙 𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟙 𝟙 ≤ω 𝟘 → refl
≤ω 𝟙 𝟙 ≤ω 𝟙 → refl
≤ω 𝟙 𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟙 𝟙 ≤ω ≤ω → refl
≤ω 𝟙 ≤𝟙 𝟘 𝟘 → refl
≤ω 𝟙 ≤𝟙 𝟘 𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟘 ≤ω → refl
≤ω 𝟙 ≤𝟙 𝟙 𝟘 → refl
≤ω 𝟙 ≤𝟙 𝟙 𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 𝟙 ≤ω → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω 𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤ω 𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω 𝟙 ≤𝟙 ≤ω ≤ω → refl
≤ω 𝟙 ≤ω 𝟘 𝟘 → refl
≤ω 𝟙 ≤ω 𝟘 𝟙 → refl
≤ω 𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤ω 𝟙 ≤ω 𝟘 ≤ω → refl
≤ω 𝟙 ≤ω 𝟙 𝟘 → refl
≤ω 𝟙 ≤ω 𝟙 𝟙 → refl
≤ω 𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤ω 𝟙 ≤ω → refl
≤ω 𝟙 ≤ω ≤𝟙 𝟘 → refl
≤ω 𝟙 ≤ω ≤𝟙 𝟙 → refl
≤ω 𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω 𝟙 ≤ω ≤𝟙 ≤ω → refl
≤ω 𝟙 ≤ω ≤ω 𝟘 → refl
≤ω 𝟙 ≤ω ≤ω 𝟙 → refl
≤ω 𝟙 ≤ω ≤ω ≤𝟙 → refl
≤ω 𝟙 ≤ω ≤ω ≤ω → refl
≤ω ≤𝟙 𝟘 𝟘 𝟘 → refl
≤ω ≤𝟙 𝟘 𝟘 𝟙 → refl
≤ω ≤𝟙 𝟘 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 𝟘 ≤ω → refl
≤ω ≤𝟙 𝟘 𝟙 𝟘 → refl
≤ω ≤𝟙 𝟘 𝟙 𝟙 → refl
≤ω ≤𝟙 𝟘 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 𝟙 ≤ω → refl
≤ω ≤𝟙 𝟘 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟘 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 𝟘 ≤ω 𝟘 → refl
≤ω ≤𝟙 𝟘 ≤ω 𝟙 → refl
≤ω ≤𝟙 𝟘 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 𝟘 ≤ω ≤ω → refl
≤ω ≤𝟙 𝟙 𝟘 𝟘 → refl
≤ω ≤𝟙 𝟙 𝟘 𝟙 → refl
≤ω ≤𝟙 𝟙 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 𝟘 ≤ω → refl
≤ω ≤𝟙 𝟙 𝟙 𝟘 → refl
≤ω ≤𝟙 𝟙 𝟙 𝟙 → refl
≤ω ≤𝟙 𝟙 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 𝟙 ≤ω → refl
≤ω ≤𝟙 𝟙 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 𝟙 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 𝟙 ≤ω 𝟘 → refl
≤ω ≤𝟙 𝟙 ≤ω 𝟙 → refl
≤ω ≤𝟙 𝟙 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 𝟙 ≤ω ≤ω → refl
≤ω ≤𝟙 ≤𝟙 𝟘 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟘 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 𝟙 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 𝟙 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤𝟙 ≤ω → refl
≤ω ≤𝟙 ≤𝟙 ≤ω 𝟘 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω 𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω ≤𝟙 → refl
≤ω ≤𝟙 ≤𝟙 ≤ω ≤ω → refl
≤ω ≤𝟙 ≤ω 𝟘 𝟘 → refl
≤ω ≤𝟙 ≤ω 𝟘 𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟘 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟘 ≤ω → refl
≤ω ≤𝟙 ≤ω 𝟙 𝟘 → refl
≤ω ≤𝟙 ≤ω 𝟙 𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω 𝟙 ≤ω → refl
≤ω ≤𝟙 ≤ω ≤𝟙 𝟘 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 𝟙 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 ≤𝟙 → refl
≤ω ≤𝟙 ≤ω ≤𝟙 ≤ω → refl
≤ω ≤𝟙 ≤ω ≤ω 𝟘 → refl
≤ω ≤𝟙 ≤ω ≤ω 𝟙 → refl
≤ω ≤𝟙 ≤ω ≤ω ≤𝟙 → refl
≤ω ≤𝟙 ≤ω ≤ω ≤ω → refl
≤ω ≤ω 𝟘 𝟘 𝟘 → refl
≤ω ≤ω 𝟘 𝟘 𝟙 → refl
≤ω ≤ω 𝟘 𝟘 ≤𝟙 → refl
≤ω ≤ω 𝟘 𝟘 ≤ω → refl
≤ω ≤ω 𝟘 𝟙 𝟘 → refl
≤ω ≤ω 𝟘 𝟙 𝟙 → refl
≤ω ≤ω 𝟘 𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟘 𝟙 ≤ω → refl
≤ω ≤ω 𝟘 ≤𝟙 𝟘 → refl
≤ω ≤ω 𝟘 ≤𝟙 𝟙 → refl
≤ω ≤ω 𝟘 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟘 ≤𝟙 ≤ω → refl
≤ω ≤ω 𝟘 ≤ω 𝟘 → refl
≤ω ≤ω 𝟘 ≤ω 𝟙 → refl
≤ω ≤ω 𝟘 ≤ω ≤𝟙 → refl
≤ω ≤ω 𝟘 ≤ω ≤ω → refl
≤ω ≤ω 𝟙 𝟘 𝟘 → refl
≤ω ≤ω 𝟙 𝟘 𝟙 → refl
≤ω ≤ω 𝟙 𝟘 ≤𝟙 → refl
≤ω ≤ω 𝟙 𝟘 ≤ω → refl
≤ω ≤ω 𝟙 𝟙 𝟘 → refl
≤ω ≤ω 𝟙 𝟙 𝟙 → refl
≤ω ≤ω 𝟙 𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟙 𝟙 ≤ω → refl
≤ω ≤ω 𝟙 ≤𝟙 𝟘 → refl
≤ω ≤ω 𝟙 ≤𝟙 𝟙 → refl
≤ω ≤ω 𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω 𝟙 ≤𝟙 ≤ω → refl
≤ω ≤ω 𝟙 ≤ω 𝟘 → refl
≤ω ≤ω 𝟙 ≤ω 𝟙 → refl
≤ω ≤ω 𝟙 ≤ω ≤𝟙 → refl
≤ω ≤ω 𝟙 ≤ω ≤ω → refl
≤ω ≤ω ≤𝟙 𝟘 𝟘 → refl
≤ω ≤ω ≤𝟙 𝟘 𝟙 → refl
≤ω ≤ω ≤𝟙 𝟘 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 𝟘 ≤ω → refl
≤ω ≤ω ≤𝟙 𝟙 𝟘 → refl
≤ω ≤ω ≤𝟙 𝟙 𝟙 → refl
≤ω ≤ω ≤𝟙 𝟙 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 𝟙 ≤ω → refl
≤ω ≤ω ≤𝟙 ≤𝟙 𝟘 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 𝟙 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 ≤𝟙 → refl
≤ω ≤ω ≤𝟙 ≤𝟙 ≤ω → refl
≤ω ≤ω ≤𝟙 ≤ω 𝟘 → refl
≤ω ≤ω ≤𝟙 ≤ω 𝟙 → refl
≤ω ≤ω ≤𝟙 ≤ω ≤𝟙 → refl
≤ω ≤ω ≤𝟙 ≤ω ≤ω → refl
≤ω ≤ω ≤ω 𝟘 𝟘 → refl
≤ω ≤ω ≤ω 𝟘 𝟙 → refl
≤ω ≤ω ≤ω 𝟘 ≤𝟙 → refl
≤ω ≤ω ≤ω 𝟘 ≤ω → refl
≤ω ≤ω ≤ω 𝟙 𝟘 → refl
≤ω ≤ω ≤ω 𝟙 𝟙 → refl
≤ω ≤ω ≤ω 𝟙 ≤𝟙 → refl
≤ω ≤ω ≤ω 𝟙 ≤ω → refl
≤ω ≤ω ≤ω ≤𝟙 𝟘 → refl
≤ω ≤ω ≤ω ≤𝟙 𝟙 → refl
≤ω ≤ω ≤ω ≤𝟙 ≤𝟙 → refl
≤ω ≤ω ≤ω ≤𝟙 ≤ω → refl
≤ω ≤ω ≤ω ≤ω 𝟘 → refl
≤ω ≤ω ≤ω ≤ω 𝟙 → refl
≤ω ≤ω ≤ω ≤ω ≤𝟙 → refl
≤ω ≤ω ≤ω ≤ω ≤ω → refl
opaque
linear-or-affine⇨affine-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(linear-or-affine v₁)
(affineModality v₂)
linear-or-affine→affine
linear-or-affine⇨affine-no-nr-preserving {v₁ = record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ LA.linear-or-affine-has-well-behaved-zero
where
open Is-no-nr-preserving-morphism
opaque
linear-or-affine⇨affine-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(linear-or-affine v₁)
(affineModality v₂)
linear-or-affine→affine
linear-or-affine⇨affine-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , A.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , A.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
affine⇨linearity-nr-preserving :
Is-nr-preserving-morphism
(affineModality v₁)
(linearityModality v₂)
⦃ A.zero-one-many-has-nr ⦄
⦃ L.zero-one-many-has-nr ⦄
affine→linearity
affine⇨linearity-nr-preserving {v₂} = λ where
.tr-nr {r} → ≤-reflexive (tr-nr′ _ r _ _ _)
where
open Is-nr-preserving-morphism
open Graded.Modality.Properties (linearityModality v₂)
tr : Affine → Linearity
tr = affine→linearity
tr-nr′ :
∀ p r z s n →
tr (A.nr p r z s n) ≡
L.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ω → refl
𝟘 𝟘 𝟘 ω 𝟘 → refl
𝟘 𝟘 𝟘 ω 𝟙 → refl
𝟘 𝟘 𝟘 ω ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ω → refl
𝟘 𝟘 𝟙 ω 𝟘 → refl
𝟘 𝟘 𝟙 ω 𝟙 → refl
𝟘 𝟘 𝟙 ω ω → refl
𝟘 𝟘 ω 𝟘 𝟘 → refl
𝟘 𝟘 ω 𝟘 𝟙 → refl
𝟘 𝟘 ω 𝟘 ω → refl
𝟘 𝟘 ω 𝟙 𝟘 → refl
𝟘 𝟘 ω 𝟙 𝟙 → refl
𝟘 𝟘 ω 𝟙 ω → refl
𝟘 𝟘 ω ω 𝟘 → refl
𝟘 𝟘 ω ω 𝟙 → refl
𝟘 𝟘 ω ω ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ω → refl
𝟘 𝟙 𝟘 ω 𝟘 → refl
𝟘 𝟙 𝟘 ω 𝟙 → refl
𝟘 𝟙 𝟘 ω ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ω → refl
𝟘 𝟙 𝟙 ω 𝟘 → refl
𝟘 𝟙 𝟙 ω 𝟙 → refl
𝟘 𝟙 𝟙 ω ω → refl
𝟘 𝟙 ω 𝟘 𝟘 → refl
𝟘 𝟙 ω 𝟘 𝟙 → refl
𝟘 𝟙 ω 𝟘 ω → refl
𝟘 𝟙 ω 𝟙 𝟘 → refl
𝟘 𝟙 ω 𝟙 𝟙 → refl
𝟘 𝟙 ω 𝟙 ω → refl
𝟘 𝟙 ω ω 𝟘 → refl
𝟘 𝟙 ω ω 𝟙 → refl
𝟘 𝟙 ω ω ω → refl
𝟘 ω 𝟘 𝟘 𝟘 → refl
𝟘 ω 𝟘 𝟘 𝟙 → refl
𝟘 ω 𝟘 𝟘 ω → refl
𝟘 ω 𝟘 𝟙 𝟘 → refl
𝟘 ω 𝟘 𝟙 𝟙 → refl
𝟘 ω 𝟘 𝟙 ω → refl
𝟘 ω 𝟘 ω 𝟘 → refl
𝟘 ω 𝟘 ω 𝟙 → refl
𝟘 ω 𝟘 ω ω → refl
𝟘 ω 𝟙 𝟘 𝟘 → refl
𝟘 ω 𝟙 𝟘 𝟙 → refl
𝟘 ω 𝟙 𝟘 ω → refl
𝟘 ω 𝟙 𝟙 𝟘 → refl
𝟘 ω 𝟙 𝟙 𝟙 → refl
𝟘 ω 𝟙 𝟙 ω → refl
𝟘 ω 𝟙 ω 𝟘 → refl
𝟘 ω 𝟙 ω 𝟙 → refl
𝟘 ω 𝟙 ω ω → refl
𝟘 ω ω 𝟘 𝟘 → refl
𝟘 ω ω 𝟘 𝟙 → refl
𝟘 ω ω 𝟘 ω → refl
𝟘 ω ω 𝟙 𝟘 → refl
𝟘 ω ω 𝟙 𝟙 → refl
𝟘 ω ω 𝟙 ω → refl
𝟘 ω ω ω 𝟘 → refl
𝟘 ω ω ω 𝟙 → refl
𝟘 ω ω ω ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ω → refl
𝟙 𝟘 𝟘 ω 𝟘 → refl
𝟙 𝟘 𝟘 ω 𝟙 → refl
𝟙 𝟘 𝟘 ω ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ω → refl
𝟙 𝟘 𝟙 ω 𝟘 → refl
𝟙 𝟘 𝟙 ω 𝟙 → refl
𝟙 𝟘 𝟙 ω ω → refl
𝟙 𝟘 ω 𝟘 𝟘 → refl
𝟙 𝟘 ω 𝟘 𝟙 → refl
𝟙 𝟘 ω 𝟘 ω → refl
𝟙 𝟘 ω 𝟙 𝟘 → refl
𝟙 𝟘 ω 𝟙 𝟙 → refl
𝟙 𝟘 ω 𝟙 ω → refl
𝟙 𝟘 ω ω 𝟘 → refl
𝟙 𝟘 ω ω 𝟙 → refl
𝟙 𝟘 ω ω ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ω → refl
𝟙 𝟙 𝟘 ω 𝟘 → refl
𝟙 𝟙 𝟘 ω 𝟙 → refl
𝟙 𝟙 𝟘 ω ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ω → refl
𝟙 𝟙 𝟙 ω 𝟘 → refl
𝟙 𝟙 𝟙 ω 𝟙 → refl
𝟙 𝟙 𝟙 ω ω → refl
𝟙 𝟙 ω 𝟘 𝟘 → refl
𝟙 𝟙 ω 𝟘 𝟙 → refl
𝟙 𝟙 ω 𝟘 ω → refl
𝟙 𝟙 ω 𝟙 𝟘 → refl
𝟙 𝟙 ω 𝟙 𝟙 → refl
𝟙 𝟙 ω 𝟙 ω → refl
𝟙 𝟙 ω ω 𝟘 → refl
𝟙 𝟙 ω ω 𝟙 → refl
𝟙 𝟙 ω ω ω → refl
𝟙 ω 𝟘 𝟘 𝟘 → refl
𝟙 ω 𝟘 𝟘 𝟙 → refl
𝟙 ω 𝟘 𝟘 ω → refl
𝟙 ω 𝟘 𝟙 𝟘 → refl
𝟙 ω 𝟘 𝟙 𝟙 → refl
𝟙 ω 𝟘 𝟙 ω → refl
𝟙 ω 𝟘 ω 𝟘 → refl
𝟙 ω 𝟘 ω 𝟙 → refl
𝟙 ω 𝟘 ω ω → refl
𝟙 ω 𝟙 𝟘 𝟘 → refl
𝟙 ω 𝟙 𝟘 𝟙 → refl
𝟙 ω 𝟙 𝟘 ω → refl
𝟙 ω 𝟙 𝟙 𝟘 → refl
𝟙 ω 𝟙 𝟙 𝟙 → refl
𝟙 ω 𝟙 𝟙 ω → refl
𝟙 ω 𝟙 ω 𝟘 → refl
𝟙 ω 𝟙 ω 𝟙 → refl
𝟙 ω 𝟙 ω ω → refl
𝟙 ω ω 𝟘 𝟘 → refl
𝟙 ω ω 𝟘 𝟙 → refl
𝟙 ω ω 𝟘 ω → refl
𝟙 ω ω 𝟙 𝟘 → refl
𝟙 ω ω 𝟙 𝟙 → refl
𝟙 ω ω 𝟙 ω → refl
𝟙 ω ω ω 𝟘 → refl
𝟙 ω ω ω 𝟙 → refl
𝟙 ω ω ω ω → refl
ω 𝟘 𝟘 𝟘 𝟘 → refl
ω 𝟘 𝟘 𝟘 𝟙 → refl
ω 𝟘 𝟘 𝟘 ω → refl
ω 𝟘 𝟘 𝟙 𝟘 → refl
ω 𝟘 𝟘 𝟙 𝟙 → refl
ω 𝟘 𝟘 𝟙 ω → refl
ω 𝟘 𝟘 ω 𝟘 → refl
ω 𝟘 𝟘 ω 𝟙 → refl
ω 𝟘 𝟘 ω ω → refl
ω 𝟘 𝟙 𝟘 𝟘 → refl
ω 𝟘 𝟙 𝟘 𝟙 → refl
ω 𝟘 𝟙 𝟘 ω → refl
ω 𝟘 𝟙 𝟙 𝟘 → refl
ω 𝟘 𝟙 𝟙 𝟙 → refl
ω 𝟘 𝟙 𝟙 ω → refl
ω 𝟘 𝟙 ω 𝟘 → refl
ω 𝟘 𝟙 ω 𝟙 → refl
ω 𝟘 𝟙 ω ω → refl
ω 𝟘 ω 𝟘 𝟘 → refl
ω 𝟘 ω 𝟘 𝟙 → refl
ω 𝟘 ω 𝟘 ω → refl
ω 𝟘 ω 𝟙 𝟘 → refl
ω 𝟘 ω 𝟙 𝟙 → refl
ω 𝟘 ω 𝟙 ω → refl
ω 𝟘 ω ω 𝟘 → refl
ω 𝟘 ω ω 𝟙 → refl
ω 𝟘 ω ω ω → refl
ω 𝟙 𝟘 𝟘 𝟘 → refl
ω 𝟙 𝟘 𝟘 𝟙 → refl
ω 𝟙 𝟘 𝟘 ω → refl
ω 𝟙 𝟘 𝟙 𝟘 → refl
ω 𝟙 𝟘 𝟙 𝟙 → refl
ω 𝟙 𝟘 𝟙 ω → refl
ω 𝟙 𝟘 ω 𝟘 → refl
ω 𝟙 𝟘 ω 𝟙 → refl
ω 𝟙 𝟘 ω ω → refl
ω 𝟙 𝟙 𝟘 𝟘 → refl
ω 𝟙 𝟙 𝟘 𝟙 → refl
ω 𝟙 𝟙 𝟘 ω → refl
ω 𝟙 𝟙 𝟙 𝟘 → refl
ω 𝟙 𝟙 𝟙 𝟙 → refl
ω 𝟙 𝟙 𝟙 ω → refl
ω 𝟙 𝟙 ω 𝟘 → refl
ω 𝟙 𝟙 ω 𝟙 → refl
ω 𝟙 𝟙 ω ω → refl
ω 𝟙 ω 𝟘 𝟘 → refl
ω 𝟙 ω 𝟘 𝟙 → refl
ω 𝟙 ω 𝟘 ω → refl
ω 𝟙 ω 𝟙 𝟘 → refl
ω 𝟙 ω 𝟙 𝟙 → refl
ω 𝟙 ω 𝟙 ω → refl
ω 𝟙 ω ω 𝟘 → refl
ω 𝟙 ω ω 𝟙 → refl
ω 𝟙 ω ω ω → refl
ω ω 𝟘 𝟘 𝟘 → refl
ω ω 𝟘 𝟘 𝟙 → refl
ω ω 𝟘 𝟘 ω → refl
ω ω 𝟘 𝟙 𝟘 → refl
ω ω 𝟘 𝟙 𝟙 → refl
ω ω 𝟘 𝟙 ω → refl
ω ω 𝟘 ω 𝟘 → refl
ω ω 𝟘 ω 𝟙 → refl
ω ω 𝟘 ω ω → refl
ω ω 𝟙 𝟘 𝟘 → refl
ω ω 𝟙 𝟘 𝟙 → refl
ω ω 𝟙 𝟘 ω → refl
ω ω 𝟙 𝟙 𝟘 → refl
ω ω 𝟙 𝟙 𝟙 → refl
ω ω 𝟙 𝟙 ω → refl
ω ω 𝟙 ω 𝟘 → refl
ω ω 𝟙 ω 𝟙 → refl
ω ω 𝟙 ω ω → refl
ω ω ω 𝟘 𝟘 → refl
ω ω ω 𝟘 𝟙 → refl
ω ω ω 𝟘 ω → refl
ω ω ω 𝟙 𝟘 → refl
ω ω ω 𝟙 𝟙 → refl
ω ω ω 𝟙 ω → refl
ω ω ω ω 𝟘 → refl
ω ω ω ω 𝟙 → refl
ω ω ω ω ω → refl
opaque
affine⇨linearity-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(affineModality v₁)
(linearityModality v₂)
affine→linearity
affine⇨linearity-no-nr-preserving {v₁ = v₁@record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ (A.affine-has-well-behaved-zero v₁)
where
open Is-no-nr-preserving-morphism
opaque
affine⇨linearity-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(affineModality v₁)
(linearityModality v₂)
affine→linearity
affine⇨linearity-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , L.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , L.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
linearity⇨affine-nr-preserving :
Is-nr-preserving-morphism
(linearityModality v₂)
(affineModality v₁)
⦃ L.zero-one-many-has-nr ⦄
⦃ A.zero-one-many-has-nr ⦄
linearity→affine
linearity⇨affine-nr-preserving = λ where
.tr-nr {r} → tr-nr′ _ r _ _ _
where
open Is-nr-preserving-morphism
tr : Linearity → Affine
tr = linearity→affine
tr-nr′ :
∀ p r z s n →
tr (L.nr p r z s n) A.≤
A.nr (tr p) (tr r) (tr z) (tr s) (tr n)
tr-nr′ = λ where
𝟘 𝟘 𝟘 𝟘 𝟘 → refl
𝟘 𝟘 𝟘 𝟘 𝟙 → refl
𝟘 𝟘 𝟘 𝟘 ω → refl
𝟘 𝟘 𝟘 𝟙 𝟘 → refl
𝟘 𝟘 𝟘 𝟙 𝟙 → refl
𝟘 𝟘 𝟘 𝟙 ω → refl
𝟘 𝟘 𝟘 ω 𝟘 → refl
𝟘 𝟘 𝟘 ω 𝟙 → refl
𝟘 𝟘 𝟘 ω ω → refl
𝟘 𝟘 𝟙 𝟘 𝟘 → refl
𝟘 𝟘 𝟙 𝟘 𝟙 → refl
𝟘 𝟘 𝟙 𝟘 ω → refl
𝟘 𝟘 𝟙 𝟙 𝟘 → refl
𝟘 𝟘 𝟙 𝟙 𝟙 → refl
𝟘 𝟘 𝟙 𝟙 ω → refl
𝟘 𝟘 𝟙 ω 𝟘 → refl
𝟘 𝟘 𝟙 ω 𝟙 → refl
𝟘 𝟘 𝟙 ω ω → refl
𝟘 𝟘 ω 𝟘 𝟘 → refl
𝟘 𝟘 ω 𝟘 𝟙 → refl
𝟘 𝟘 ω 𝟘 ω → refl
𝟘 𝟘 ω 𝟙 𝟘 → refl
𝟘 𝟘 ω 𝟙 𝟙 → refl
𝟘 𝟘 ω 𝟙 ω → refl
𝟘 𝟘 ω ω 𝟘 → refl
𝟘 𝟘 ω ω 𝟙 → refl
𝟘 𝟘 ω ω ω → refl
𝟘 𝟙 𝟘 𝟘 𝟘 → refl
𝟘 𝟙 𝟘 𝟘 𝟙 → refl
𝟘 𝟙 𝟘 𝟘 ω → refl
𝟘 𝟙 𝟘 𝟙 𝟘 → refl
𝟘 𝟙 𝟘 𝟙 𝟙 → refl
𝟘 𝟙 𝟘 𝟙 ω → refl
𝟘 𝟙 𝟘 ω 𝟘 → refl
𝟘 𝟙 𝟘 ω 𝟙 → refl
𝟘 𝟙 𝟘 ω ω → refl
𝟘 𝟙 𝟙 𝟘 𝟘 → refl
𝟘 𝟙 𝟙 𝟘 𝟙 → refl
𝟘 𝟙 𝟙 𝟘 ω → refl
𝟘 𝟙 𝟙 𝟙 𝟘 → refl
𝟘 𝟙 𝟙 𝟙 𝟙 → refl
𝟘 𝟙 𝟙 𝟙 ω → refl
𝟘 𝟙 𝟙 ω 𝟘 → refl
𝟘 𝟙 𝟙 ω 𝟙 → refl
𝟘 𝟙 𝟙 ω ω → refl
𝟘 𝟙 ω 𝟘 𝟘 → refl
𝟘 𝟙 ω 𝟘 𝟙 → refl
𝟘 𝟙 ω 𝟘 ω → refl
𝟘 𝟙 ω 𝟙 𝟘 → refl
𝟘 𝟙 ω 𝟙 𝟙 → refl
𝟘 𝟙 ω 𝟙 ω → refl
𝟘 𝟙 ω ω 𝟘 → refl
𝟘 𝟙 ω ω 𝟙 → refl
𝟘 𝟙 ω ω ω → refl
𝟘 ω 𝟘 𝟘 𝟘 → refl
𝟘 ω 𝟘 𝟘 𝟙 → refl
𝟘 ω 𝟘 𝟘 ω → refl
𝟘 ω 𝟘 𝟙 𝟘 → refl
𝟘 ω 𝟘 𝟙 𝟙 → refl
𝟘 ω 𝟘 𝟙 ω → refl
𝟘 ω 𝟘 ω 𝟘 → refl
𝟘 ω 𝟘 ω 𝟙 → refl
𝟘 ω 𝟘 ω ω → refl
𝟘 ω 𝟙 𝟘 𝟘 → refl
𝟘 ω 𝟙 𝟘 𝟙 → refl
𝟘 ω 𝟙 𝟘 ω → refl
𝟘 ω 𝟙 𝟙 𝟘 → refl
𝟘 ω 𝟙 𝟙 𝟙 → refl
𝟘 ω 𝟙 𝟙 ω → refl
𝟘 ω 𝟙 ω 𝟘 → refl
𝟘 ω 𝟙 ω 𝟙 → refl
𝟘 ω 𝟙 ω ω → refl
𝟘 ω ω 𝟘 𝟘 → refl
𝟘 ω ω 𝟘 𝟙 → refl
𝟘 ω ω 𝟘 ω → refl
𝟘 ω ω 𝟙 𝟘 → refl
𝟘 ω ω 𝟙 𝟙 → refl
𝟘 ω ω 𝟙 ω → refl
𝟘 ω ω ω 𝟘 → refl
𝟘 ω ω ω 𝟙 → refl
𝟘 ω ω ω ω → refl
𝟙 𝟘 𝟘 𝟘 𝟘 → refl
𝟙 𝟘 𝟘 𝟘 𝟙 → refl
𝟙 𝟘 𝟘 𝟘 ω → refl
𝟙 𝟘 𝟘 𝟙 𝟘 → refl
𝟙 𝟘 𝟘 𝟙 𝟙 → refl
𝟙 𝟘 𝟘 𝟙 ω → refl
𝟙 𝟘 𝟘 ω 𝟘 → refl
𝟙 𝟘 𝟘 ω 𝟙 → refl
𝟙 𝟘 𝟘 ω ω → refl
𝟙 𝟘 𝟙 𝟘 𝟘 → refl
𝟙 𝟘 𝟙 𝟘 𝟙 → refl
𝟙 𝟘 𝟙 𝟘 ω → refl
𝟙 𝟘 𝟙 𝟙 𝟘 → refl
𝟙 𝟘 𝟙 𝟙 𝟙 → refl
𝟙 𝟘 𝟙 𝟙 ω → refl
𝟙 𝟘 𝟙 ω 𝟘 → refl
𝟙 𝟘 𝟙 ω 𝟙 → refl
𝟙 𝟘 𝟙 ω ω → refl
𝟙 𝟘 ω 𝟘 𝟘 → refl
𝟙 𝟘 ω 𝟘 𝟙 → refl
𝟙 𝟘 ω 𝟘 ω → refl
𝟙 𝟘 ω 𝟙 𝟘 → refl
𝟙 𝟘 ω 𝟙 𝟙 → refl
𝟙 𝟘 ω 𝟙 ω → refl
𝟙 𝟘 ω ω 𝟘 → refl
𝟙 𝟘 ω ω 𝟙 → refl
𝟙 𝟘 ω ω ω → refl
𝟙 𝟙 𝟘 𝟘 𝟘 → refl
𝟙 𝟙 𝟘 𝟘 𝟙 → refl
𝟙 𝟙 𝟘 𝟘 ω → refl
𝟙 𝟙 𝟘 𝟙 𝟘 → refl
𝟙 𝟙 𝟘 𝟙 𝟙 → refl
𝟙 𝟙 𝟘 𝟙 ω → refl
𝟙 𝟙 𝟘 ω 𝟘 → refl
𝟙 𝟙 𝟘 ω 𝟙 → refl
𝟙 𝟙 𝟘 ω ω → refl
𝟙 𝟙 𝟙 𝟘 𝟘 → refl
𝟙 𝟙 𝟙 𝟘 𝟙 → refl
𝟙 𝟙 𝟙 𝟘 ω → refl
𝟙 𝟙 𝟙 𝟙 𝟘 → refl
𝟙 𝟙 𝟙 𝟙 𝟙 → refl
𝟙 𝟙 𝟙 𝟙 ω → refl
𝟙 𝟙 𝟙 ω 𝟘 → refl
𝟙 𝟙 𝟙 ω 𝟙 → refl
𝟙 𝟙 𝟙 ω ω → refl
𝟙 𝟙 ω 𝟘 𝟘 → refl
𝟙 𝟙 ω 𝟘 𝟙 → refl
𝟙 𝟙 ω 𝟘 ω → refl
𝟙 𝟙 ω 𝟙 𝟘 → refl
𝟙 𝟙 ω 𝟙 𝟙 → refl
𝟙 𝟙 ω 𝟙 ω → refl
𝟙 𝟙 ω ω 𝟘 → refl
𝟙 𝟙 ω ω 𝟙 → refl
𝟙 𝟙 ω ω ω → refl
𝟙 ω 𝟘 𝟘 𝟘 → refl
𝟙 ω 𝟘 𝟘 𝟙 → refl
𝟙 ω 𝟘 𝟘 ω → refl
𝟙 ω 𝟘 𝟙 𝟘 → refl
𝟙 ω 𝟘 𝟙 𝟙 → refl
𝟙 ω 𝟘 𝟙 ω → refl
𝟙 ω 𝟘 ω 𝟘 → refl
𝟙 ω 𝟘 ω 𝟙 → refl
𝟙 ω 𝟘 ω ω → refl
𝟙 ω 𝟙 𝟘 𝟘 → refl
𝟙 ω 𝟙 𝟘 𝟙 → refl
𝟙 ω 𝟙 𝟘 ω → refl
𝟙 ω 𝟙 𝟙 𝟘 → refl
𝟙 ω 𝟙 𝟙 𝟙 → refl
𝟙 ω 𝟙 𝟙 ω → refl
𝟙 ω 𝟙 ω 𝟘 → refl
𝟙 ω 𝟙 ω 𝟙 → refl
𝟙 ω 𝟙 ω ω → refl
𝟙 ω ω 𝟘 𝟘 → refl
𝟙 ω ω 𝟘 𝟙 → refl
𝟙 ω ω 𝟘 ω → refl
𝟙 ω ω 𝟙 𝟘 → refl
𝟙 ω ω 𝟙 𝟙 → refl
𝟙 ω ω 𝟙 ω → refl
𝟙 ω ω ω 𝟘 → refl
𝟙 ω ω ω 𝟙 → refl
𝟙 ω ω ω ω → refl
ω 𝟘 𝟘 𝟘 𝟘 → refl
ω 𝟘 𝟘 𝟘 𝟙 → refl
ω 𝟘 𝟘 𝟘 ω → refl
ω 𝟘 𝟘 𝟙 𝟘 → refl
ω 𝟘 𝟘 𝟙 𝟙 → refl
ω 𝟘 𝟘 𝟙 ω → refl
ω 𝟘 𝟘 ω 𝟘 → refl
ω 𝟘 𝟘 ω 𝟙 → refl
ω 𝟘 𝟘 ω ω → refl
ω 𝟘 𝟙 𝟘 𝟘 → refl
ω 𝟘 𝟙 𝟘 𝟙 → refl
ω 𝟘 𝟙 𝟘 ω → refl
ω 𝟘 𝟙 𝟙 𝟘 → refl
ω 𝟘 𝟙 𝟙 𝟙 → refl
ω 𝟘 𝟙 𝟙 ω → refl
ω 𝟘 𝟙 ω 𝟘 → refl
ω 𝟘 𝟙 ω 𝟙 → refl
ω 𝟘 𝟙 ω ω → refl
ω 𝟘 ω 𝟘 𝟘 → refl
ω 𝟘 ω 𝟘 𝟙 → refl
ω 𝟘 ω 𝟘 ω → refl
ω 𝟘 ω 𝟙 𝟘 → refl
ω 𝟘 ω 𝟙 𝟙 → refl
ω 𝟘 ω 𝟙 ω → refl
ω 𝟘 ω ω 𝟘 → refl
ω 𝟘 ω ω 𝟙 → refl
ω 𝟘 ω ω ω → refl
ω 𝟙 𝟘 𝟘 𝟘 → refl
ω 𝟙 𝟘 𝟘 𝟙 → refl
ω 𝟙 𝟘 𝟘 ω → refl
ω 𝟙 𝟘 𝟙 𝟘 → refl
ω 𝟙 𝟘 𝟙 𝟙 → refl
ω 𝟙 𝟘 𝟙 ω → refl
ω 𝟙 𝟘 ω 𝟘 → refl
ω 𝟙 𝟘 ω 𝟙 → refl
ω 𝟙 𝟘 ω ω → refl
ω 𝟙 𝟙 𝟘 𝟘 → refl
ω 𝟙 𝟙 𝟘 𝟙 → refl
ω 𝟙 𝟙 𝟘 ω → refl
ω 𝟙 𝟙 𝟙 𝟘 → refl
ω 𝟙 𝟙 𝟙 𝟙 → refl
ω 𝟙 𝟙 𝟙 ω → refl
ω 𝟙 𝟙 ω 𝟘 → refl
ω 𝟙 𝟙 ω 𝟙 → refl
ω 𝟙 𝟙 ω ω → refl
ω 𝟙 ω 𝟘 𝟘 → refl
ω 𝟙 ω 𝟘 𝟙 → refl
ω 𝟙 ω 𝟘 ω → refl
ω 𝟙 ω 𝟙 𝟘 → refl
ω 𝟙 ω 𝟙 𝟙 → refl
ω 𝟙 ω 𝟙 ω → refl
ω 𝟙 ω ω 𝟘 → refl
ω 𝟙 ω ω 𝟙 → refl
ω 𝟙 ω ω ω → refl
ω ω 𝟘 𝟘 𝟘 → refl
ω ω 𝟘 𝟘 𝟙 → refl
ω ω 𝟘 𝟘 ω → refl
ω ω 𝟘 𝟙 𝟘 → refl
ω ω 𝟘 𝟙 𝟙 → refl
ω ω 𝟘 𝟙 ω → refl
ω ω 𝟘 ω 𝟘 → refl
ω ω 𝟘 ω 𝟙 → refl
ω ω 𝟘 ω ω → refl
ω ω 𝟙 𝟘 𝟘 → refl
ω ω 𝟙 𝟘 𝟙 → refl
ω ω 𝟙 𝟘 ω → refl
ω ω 𝟙 𝟙 𝟘 → refl
ω ω 𝟙 𝟙 𝟙 → refl
ω ω 𝟙 𝟙 ω → refl
ω ω 𝟙 ω 𝟘 → refl
ω ω 𝟙 ω 𝟙 → refl
ω ω 𝟙 ω ω → refl
ω ω ω 𝟘 𝟘 → refl
ω ω ω 𝟘 𝟙 → refl
ω ω ω 𝟘 ω → refl
ω ω ω 𝟙 𝟘 → refl
ω ω ω 𝟙 𝟙 → refl
ω ω ω 𝟙 ω → refl
ω ω ω ω 𝟘 → refl
ω ω ω ω 𝟙 → refl
ω ω ω ω ω → refl
opaque
linearity⇨affine-no-nr-preserving :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-preserving-morphism
(linearityModality v₂)
(affineModality v₁)
linearity→affine
linearity⇨affine-no-nr-preserving {v₁ = v₁@record{}} refl = λ where
.𝟘ᵐ-in-first-if-in-second → inj₁
.𝟘-well-behaved-in-first-if-in-second _ →
inj₁ (L.linearity-has-well-behaved-zero v₁)
where
open Is-no-nr-preserving-morphism
opaque
linearity⇨affine-no-nr-glb-preserving :
Is-no-nr-glb-preserving-morphism
(linearityModality v₂)
(affineModality v₁)
linearity→affine
linearity⇨affine-no-nr-glb-preserving = λ where
.tr-nrᵢ-GLB _ → _ , A.nr-nrᵢ-GLB _
.tr-nrᵢ-𝟙-GLB _ → _ , A.nr-nrᵢ-GLB _
where
open Is-no-nr-glb-preserving-morphism
opaque
unit⇒erasure-nr-reflecting :
Is-nr-reflecting-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
⦃ unit-has-nr ⦄
unit→erasure
unit⇒erasure-nr-reflecting = λ where
.tr-≤-nr _ →
_ , _ , _ , refl , refl , refl , refl
where
open Is-nr-reflecting-morphism
opaque
unit⇒erasure-no-nr-reflecting :
Is-no-nr-reflecting-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
unit→erasure
unit⇒erasure-no-nr-reflecting = λ where
.tr-≤-no-nr _ _ _ _ _ →
_ , _ , _ , _ , refl , refl , refl , refl
, refl , (λ _ → refl) , refl , refl
where
open Is-no-nr-reflecting-morphism
opaque
unit⇒erasure-no-nr-glb-reflecting :
Is-no-nr-glb-reflecting-morphism
(UnitModality v₁ v₁-ok)
(ErasureModality v₂)
unit→erasure
unit⇒erasure-no-nr-glb-reflecting {v₁} {v₁-ok} = λ where
.tr-≤-no-nr _ _ _ →
_ , _ , _ , _ , _ , refl , refl , refl
, GLB-const′ , GLB-const′ , refl
.tr-nrᵢ-glb _ →
_ , GLB-const′
where
open Is-no-nr-glb-reflecting-morphism
open Graded.Modality.Properties (UnitModality v₁ v₁-ok)
opaque
erasure⇨zero-one-many-nr-reflecting :
Is-nr-reflecting-morphism
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
⦃ has-nr₂ = ZOM.zero-one-many-has-nr 𝟙≤𝟘 ⦄
erasure→zero-one-many
erasure⇨zero-one-many-nr-reflecting = λ where
.tr-≤-nr {r} → tr-≤-nr′ _ _ _ r _ _ _
where
open Is-nr-reflecting-morphism
tr-≤-nr′ :
∀ 𝟙≤𝟘 →
let module 𝟘𝟙ω′ = ZOM 𝟙≤𝟘
tr = erasure→zero-one-many in
∀ q p r z₁ s₁ n₁ →
tr q 𝟘𝟙ω′.≤ 𝟘𝟙ω′.nr (tr p) (tr r) z₁ s₁ n₁ →
∃₃ λ z₂ s₂ n₂ →
tr z₂ 𝟘𝟙ω′.≤ z₁ × tr s₂ 𝟘𝟙ω′.≤ s₁ × tr n₂ 𝟘𝟙ω′.≤ n₁ ×
q E.≤ E.nr p r z₂ s₂ n₂
tr-≤-nr′ = λ where
_ 𝟘 𝟘 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
_ 𝟘 𝟘 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
_ 𝟘 ω 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
_ 𝟘 ω ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
_ ω _ _ _ _ _ _ → ω , ω , ω , refl , refl , refl , refl
true 𝟘 𝟘 𝟘 𝟘 𝟘 𝟙 ()
false 𝟘 𝟘 𝟘 𝟘 𝟘 𝟙 ()
true 𝟘 𝟘 𝟘 𝟘 𝟘 ω ()
false 𝟘 𝟘 𝟘 𝟘 𝟘 ω ()
true 𝟘 𝟘 𝟘 𝟘 𝟙 𝟘 ()
false 𝟘 𝟘 𝟘 𝟘 𝟙 𝟘 ()
true 𝟘 𝟘 𝟘 𝟘 𝟙 𝟙 ()
false 𝟘 𝟘 𝟘 𝟘 𝟙 𝟙 ()
true 𝟘 𝟘 𝟘 𝟘 𝟙 ω ()
false 𝟘 𝟘 𝟘 𝟘 𝟙 ω ()
true 𝟘 𝟘 𝟘 𝟘 ω 𝟘 ()
false 𝟘 𝟘 𝟘 𝟘 ω 𝟘 ()
true 𝟘 𝟘 𝟘 𝟘 ω 𝟙 ()
false 𝟘 𝟘 𝟘 𝟘 ω 𝟙 ()
true 𝟘 𝟘 𝟘 𝟘 ω ω ()
false 𝟘 𝟘 𝟘 𝟘 ω ω ()
true 𝟘 𝟘 𝟘 𝟙 𝟘 𝟘 ()
false 𝟘 𝟘 𝟘 𝟙 𝟘 𝟘 ()
true 𝟘 𝟘 𝟘 𝟙 𝟘 𝟙 ()
false 𝟘 𝟘 𝟘 𝟙 𝟘 𝟙 ()
true 𝟘 𝟘 𝟘 𝟙 𝟘 ω ()
false 𝟘 𝟘 𝟘 𝟙 𝟘 ω ()
true 𝟘 𝟘 𝟘 𝟙 𝟙 𝟘 ()
false 𝟘 𝟘 𝟘 𝟙 𝟙 𝟘 ()
true 𝟘 𝟘 𝟘 𝟙 𝟙 𝟙 ()
false 𝟘 𝟘 𝟘 𝟙 𝟙 𝟙 ()
true 𝟘 𝟘 𝟘 𝟙 𝟙 ω ()
false 𝟘 𝟘 𝟘 𝟙 𝟙 ω ()
true 𝟘 𝟘 𝟘 𝟙 ω 𝟘 ()
false 𝟘 𝟘 𝟘 𝟙 ω 𝟘 ()
true 𝟘 𝟘 𝟘 𝟙 ω 𝟙 ()
false 𝟘 𝟘 𝟘 𝟙 ω 𝟙 ()
true 𝟘 𝟘 𝟘 𝟙 ω ω ()
false 𝟘 𝟘 𝟘 𝟙 ω ω ()
true 𝟘 𝟘 𝟘 ω 𝟘 𝟘 ()
false 𝟘 𝟘 𝟘 ω 𝟘 𝟘 ()
true 𝟘 𝟘 𝟘 ω 𝟘 𝟙 ()
false 𝟘 𝟘 𝟘 ω 𝟘 𝟙 ()
true 𝟘 𝟘 𝟘 ω 𝟘 ω ()
false 𝟘 𝟘 𝟘 ω 𝟘 ω ()
true 𝟘 𝟘 𝟘 ω 𝟙 𝟘 ()
false 𝟘 𝟘 𝟘 ω 𝟙 𝟘 ()
true 𝟘 𝟘 𝟘 ω 𝟙 𝟙 ()
false 𝟘 𝟘 𝟘 ω 𝟙 𝟙 ()
true 𝟘 𝟘 𝟘 ω 𝟙 ω ()
false 𝟘 𝟘 𝟘 ω 𝟙 ω ()
true 𝟘 𝟘 𝟘 ω ω 𝟘 ()
false 𝟘 𝟘 𝟘 ω ω 𝟘 ()
true 𝟘 𝟘 𝟘 ω ω 𝟙 ()
false 𝟘 𝟘 𝟘 ω ω 𝟙 ()
true 𝟘 𝟘 𝟘 ω ω ω ()
false 𝟘 𝟘 𝟘 ω ω ω ()
_ 𝟘 𝟘 ω 𝟘 𝟘 𝟙 ()
_ 𝟘 𝟘 ω 𝟘 𝟘 ω ()
_ 𝟘 𝟘 ω 𝟘 𝟙 𝟘 ()
_ 𝟘 𝟘 ω 𝟘 𝟙 𝟙 ()
_ 𝟘 𝟘 ω 𝟘 𝟙 ω ()
_ 𝟘 𝟘 ω 𝟘 ω 𝟘 ()
_ 𝟘 𝟘 ω 𝟘 ω 𝟙 ()
_ 𝟘 𝟘 ω 𝟘 ω ω ()
_ 𝟘 𝟘 ω 𝟙 𝟘 𝟘 ()
_ 𝟘 𝟘 ω 𝟙 𝟘 𝟙 ()
_ 𝟘 𝟘 ω 𝟙 𝟘 ω ()
_ 𝟘 𝟘 ω 𝟙 𝟙 𝟘 ()
_ 𝟘 𝟘 ω 𝟙 𝟙 𝟙 ()
_ 𝟘 𝟘 ω 𝟙 𝟙 ω ()
_ 𝟘 𝟘 ω 𝟙 ω 𝟘 ()
_ 𝟘 𝟘 ω 𝟙 ω 𝟙 ()
_ 𝟘 𝟘 ω 𝟙 ω ω ()
_ 𝟘 𝟘 ω ω 𝟘 𝟘 ()
_ 𝟘 𝟘 ω ω 𝟘 𝟙 ()
_ 𝟘 𝟘 ω ω 𝟘 ω ()
_ 𝟘 𝟘 ω ω 𝟙 𝟘 ()
_ 𝟘 𝟘 ω ω 𝟙 𝟙 ()
_ 𝟘 𝟘 ω ω 𝟙 ω ()
_ 𝟘 𝟘 ω ω ω 𝟘 ()
_ 𝟘 𝟘 ω ω ω 𝟙 ()
_ 𝟘 𝟘 ω ω ω ω ()
_ 𝟘 ω 𝟘 𝟘 𝟘 𝟙 ()
_ 𝟘 ω 𝟘 𝟘 𝟘 ω ()
true 𝟘 ω 𝟘 𝟘 𝟙 𝟘 ()
false 𝟘 ω 𝟘 𝟘 𝟙 𝟘 ()
_ 𝟘 ω 𝟘 𝟘 𝟙 𝟙 ()
_ 𝟘 ω 𝟘 𝟘 𝟙 ω ()
_ 𝟘 ω 𝟘 𝟘 ω 𝟘 ()
_ 𝟘 ω 𝟘 𝟘 ω 𝟙 ()
_ 𝟘 ω 𝟘 𝟘 ω ω ()
true 𝟘 ω 𝟘 𝟙 𝟘 𝟘 ()
false 𝟘 ω 𝟘 𝟙 𝟘 𝟘 ()
_ 𝟘 ω 𝟘 𝟙 𝟘 𝟙 ()
_ 𝟘 ω 𝟘 𝟙 𝟘 ω ()
true 𝟘 ω 𝟘 𝟙 𝟙 𝟘 ()
false 𝟘 ω 𝟘 𝟙 𝟙 𝟘 ()
_ 𝟘 ω 𝟘 𝟙 𝟙 𝟙 ()
_ 𝟘 ω 𝟘 𝟙 𝟙 ω ()
_ 𝟘 ω 𝟘 𝟙 ω 𝟘 ()
_ 𝟘 ω 𝟘 𝟙 ω 𝟙 ()
_ 𝟘 ω 𝟘 𝟙 ω ω ()
_ 𝟘 ω 𝟘 ω 𝟘 𝟘 ()
_ 𝟘 ω 𝟘 ω 𝟘 𝟙 ()
_ 𝟘 ω 𝟘 ω 𝟘 ω ()
_ 𝟘 ω 𝟘 ω 𝟙 𝟘 ()
_ 𝟘 ω 𝟘 ω 𝟙 𝟙 ()
_ 𝟘 ω 𝟘 ω 𝟙 ω ()
_ 𝟘 ω 𝟘 ω ω 𝟘 ()
_ 𝟘 ω 𝟘 ω ω 𝟙 ()
_ 𝟘 ω 𝟘 ω ω ω ()
_ 𝟘 ω ω 𝟘 𝟘 𝟙 ()
_ 𝟘 ω ω 𝟘 𝟘 ω ()
_ 𝟘 ω ω 𝟘 𝟙 𝟘 ()
_ 𝟘 ω ω 𝟘 𝟙 𝟙 ()
_ 𝟘 ω ω 𝟘 𝟙 ω ()
_ 𝟘 ω ω 𝟘 ω 𝟘 ()
_ 𝟘 ω ω 𝟘 ω 𝟙 ()
_ 𝟘 ω ω 𝟘 ω ω ()
_ 𝟘 ω ω 𝟙 𝟘 𝟘 ()
_ 𝟘 ω ω 𝟙 𝟘 𝟙 ()
_ 𝟘 ω ω 𝟙 𝟘 ω ()
_ 𝟘 ω ω 𝟙 𝟙 𝟘 ()
_ 𝟘 ω ω 𝟙 𝟙 𝟙 ()
_ 𝟘 ω ω 𝟙 𝟙 ω ()
_ 𝟘 ω ω 𝟙 ω 𝟘 ()
_ 𝟘 ω ω 𝟙 ω 𝟙 ()
_ 𝟘 ω ω 𝟙 ω ω ()
_ 𝟘 ω ω ω 𝟘 𝟘 ()
_ 𝟘 ω ω ω 𝟘 𝟙 ()
_ 𝟘 ω ω ω 𝟘 ω ()
_ 𝟘 ω ω ω 𝟙 𝟘 ()
_ 𝟘 ω ω ω 𝟙 𝟙 ()
_ 𝟘 ω ω ω 𝟙 ω ()
_ 𝟘 ω ω ω ω 𝟘 ()
_ 𝟘 ω ω ω ω 𝟙 ()
_ 𝟘 ω ω ω ω ω ()
opaque
erasure⇨zero-one-many-no-nr-reflecting :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-reflecting-morphism
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
erasure→zero-one-many
erasure⇨zero-one-many-no-nr-reflecting
{v₁ = v₁@record{}} {v₂} {𝟙≤𝟘} refl = λ where
.tr-≤-no-nr {r} {s} → →tr-≤-no-nr {r = r} {s = s}
(ErasureModality v₁)
(zero-one-many-modality 𝟙≤𝟘 v₂)
idᶠ
𝟘𝟙ω.zero-one-many-has-well-behaved-zero
tr tr⁻¹ tr⁻¹-monotone tr≤→≤tr⁻¹ tr-tr⁻¹≤
(λ p q → ≤-reflexive (tr⁻¹-+ p q))
(λ p q → ≤-reflexive (tr⁻¹-∧ p q))
λ p q → ≤-reflexive (tr⁻¹-· p q)
where
open Is-no-nr-reflecting-morphism
module 𝟘𝟙ω = ZOM 𝟙≤𝟘
open Graded.Modality.Properties (ErasureModality v₁)
tr : Erasure → Zero-one-many 𝟙≤𝟘
tr = erasure→zero-one-many
tr⁻¹ : Zero-one-many 𝟙≤𝟘 → Erasure
tr⁻¹ = zero-one-many→erasure
tr⁻¹-monotone :
∀ p q → p 𝟘𝟙ω.≤ q →
tr⁻¹ p E.≤ tr⁻¹ q
tr⁻¹-monotone = λ where
𝟘 𝟘 _ → refl
𝟘 𝟙 𝟘≡𝟘∧𝟙 → ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
𝟙 𝟘 _ → refl
𝟙 𝟙 _ → refl
ω 𝟘 _ → refl
ω 𝟙 _ → refl
ω ω _ → refl
𝟘 ω ()
𝟙 ω ()
tr≤→≤tr⁻¹ : ∀ p q → tr p 𝟘𝟙ω.≤ q → p E.≤ tr⁻¹ q
tr≤→≤tr⁻¹ = λ where
𝟘 𝟘 _ → refl
𝟘 𝟙 𝟘≡𝟘∧𝟙 → ⊥-elim (𝟘𝟙ω.𝟘∧𝟙≢𝟘 (sym 𝟘≡𝟘∧𝟙))
ω 𝟘 _ → refl
ω 𝟙 _ → refl
ω ω _ → refl
𝟘 ω ()
tr-tr⁻¹≤ : ∀ p → tr (tr⁻¹ p) 𝟘𝟙ω.≤ p
tr-tr⁻¹≤ = λ where
𝟘 → refl
𝟙 → refl
ω → refl
tr⁻¹-𝟘∧𝟙 : tr⁻¹ 𝟘𝟙ω.𝟘∧𝟙 ≡ ω
tr⁻¹-𝟘∧𝟙 = 𝟘𝟙ω.𝟘∧𝟙-elim
(λ p → tr⁻¹ p ≡ ω)
(λ _ → refl)
(λ _ → refl)
tr⁻¹-∧ : ∀ p q → tr⁻¹ (p 𝟘𝟙ω.∧ q) ≡ tr⁻¹ p E.∧ tr⁻¹ q
tr⁻¹-∧ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → tr⁻¹-𝟘∧𝟙
𝟘 ω → refl
𝟙 𝟘 → tr⁻¹-𝟘∧𝟙
𝟙 𝟙 → refl
𝟙 ω → refl
ω 𝟘 → refl
ω 𝟙 → refl
ω ω → refl
tr⁻¹-+ : ∀ p q → tr⁻¹ (p 𝟘𝟙ω.+ q) ≡ tr⁻¹ p E.+ tr⁻¹ q
tr⁻¹-+ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ω → refl
ω 𝟘 → refl
ω 𝟙 → refl
ω ω → refl
tr⁻¹-· : ∀ p q → tr⁻¹ (tr p 𝟘𝟙ω.· q) ≡ p E.· tr⁻¹ q
tr⁻¹-· = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ω → refl
ω 𝟘 → refl
ω 𝟙 → refl
ω ω → refl
opaque
erasure⇒linearity-nr-reflecting :
Is-nr-reflecting-morphism
(ErasureModality v₁)
(linearityModality v₂)
⦃ E.erasure-has-nr ⦄
⦃ L.zero-one-many-has-nr ⦄
erasure→zero-one-many
erasure⇒linearity-nr-reflecting = erasure⇨zero-one-many-nr-reflecting
opaque
erasure⇒affine-nr-reflecting :
Is-nr-reflecting-morphism
(ErasureModality v₁)
(affineModality v₂)
⦃ E.erasure-has-nr ⦄
⦃ A.zero-one-many-has-nr ⦄
erasure→zero-one-many
erasure⇒affine-nr-reflecting = erasure⇨zero-one-many-nr-reflecting
opaque
erasure⇒linearity-no-nr-reflecting :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-reflecting-morphism
(ErasureModality v₁)
(linearityModality v₂)
erasure→zero-one-many
erasure⇒linearity-no-nr-reflecting = erasure⇨zero-one-many-no-nr-reflecting
opaque
erasure⇒affine-no-nr-reflecting :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-reflecting-morphism
(ErasureModality v₁)
(affineModality v₂)
erasure→zero-one-many
erasure⇒affine-no-nr-reflecting = erasure⇨zero-one-many-no-nr-reflecting
opaque
linearity⇨linear-or-affine-nr-reflecting :
Is-nr-reflecting-morphism
(linearityModality v₁)
(linear-or-affine v₂)
⦃ L.zero-one-many-has-nr ⦄
⦃ LA.linear-or-affine-has-nr ⦄
linearity→linear-or-affine
linearity⇨linear-or-affine-nr-reflecting = λ where
.tr-≤-nr {r} → tr-≤-nr′ _ _ r _ _ _
where
open Is-nr-reflecting-morphism
tr : Linearity → Linear-or-affine
tr = linearity→linear-or-affine
tr-≤-nr′ :
∀ q p r z₁ s₁ n₁ →
tr q LA.≤ LA.nr (tr p) (tr r) z₁ s₁ n₁ →
∃₃ λ z₂ s₂ n₂ →
tr z₂ LA.≤ z₁ × tr s₂ LA.≤ s₁ × tr n₂ LA.≤ n₁ ×
q L.≤ L.nr p r z₂ s₂ n₂
tr-≤-nr′ = λ where
ω _ _ _ _ _ _ → ω , ω , ω , refl , refl , refl , refl
𝟘 𝟘 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟘 𝟘 𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 𝟘 𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 𝟘 𝟘 𝟘 𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟘 ≤ω ()
𝟘 𝟘 𝟘 𝟘 𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟘 𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤ω ≤ω ()
𝟘 𝟘 𝟘 𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟘 𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟘 𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 𝟘 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 𝟘 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤ω ≤ω ()
𝟘 𝟘 𝟙 𝟘 𝟘 𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟘 ≤ω ()
𝟘 𝟘 𝟙 𝟘 𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟘 𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤ω ≤ω ()
𝟘 𝟘 𝟙 𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟙 𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟙 𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 𝟘 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 𝟘 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤ω ≤ω ()
𝟘 𝟘 ω 𝟘 𝟘 𝟙 ()
𝟘 𝟘 ω 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 𝟘 ≤ω ()
𝟘 𝟘 ω 𝟘 𝟙 𝟘 ()
𝟘 𝟘 ω 𝟘 𝟙 𝟙 ()
𝟘 𝟘 ω 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 𝟙 ≤ω ()
𝟘 𝟘 ω 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 ω 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 ω 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 ω 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 ω 𝟘 ≤ω ≤ω ()
𝟘 𝟘 ω 𝟙 𝟘 𝟘 ()
𝟘 𝟘 ω 𝟙 𝟘 𝟙 ()
𝟘 𝟘 ω 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 𝟘 ≤ω ()
𝟘 𝟘 ω 𝟙 𝟙 𝟘 ()
𝟘 𝟘 ω 𝟙 𝟙 𝟙 ()
𝟘 𝟘 ω 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 𝟙 ≤ω ()
𝟘 𝟘 ω 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 ω 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 ω 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 ω 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 ω 𝟙 ≤ω ≤ω ()
𝟘 𝟘 ω ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 ω ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 ω ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 ω ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 ω ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 ω ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 ω ≤ω 𝟘 𝟘 ()
𝟘 𝟘 ω ≤ω 𝟘 𝟙 ()
𝟘 𝟘 ω ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 ω ≤ω 𝟘 ≤ω ()
𝟘 𝟘 ω ≤ω 𝟙 𝟘 ()
𝟘 𝟘 ω ≤ω 𝟙 𝟙 ()
𝟘 𝟘 ω ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤ω 𝟙 ≤ω ()
𝟘 𝟘 ω ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 ω ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 ω ≤ω ≤ω 𝟘 ()
𝟘 𝟘 ω ≤ω ≤ω 𝟙 ()
𝟘 𝟘 ω ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 ω ≤ω ≤ω ≤ω ()
𝟘 𝟙 𝟘 𝟘 𝟘 𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟘 ≤ω ()
𝟘 𝟙 𝟘 𝟘 𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟘 𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤ω ≤ω ()
𝟘 𝟙 𝟘 𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟘 𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟘 𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 𝟙 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 𝟙 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤ω ≤ω ()
𝟘 𝟙 𝟙 𝟘 𝟘 𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟘 ≤ω ()
𝟘 𝟙 𝟙 𝟘 𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟘 𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤ω ≤ω ()
𝟘 𝟙 𝟙 𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟙 𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟙 𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 𝟙 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 𝟙 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤ω ≤ω ()
𝟘 𝟙 ω 𝟘 𝟘 𝟙 ()
𝟘 𝟙 ω 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 𝟘 ≤ω ()
𝟘 𝟙 ω 𝟘 𝟙 𝟘 ()
𝟘 𝟙 ω 𝟘 𝟙 𝟙 ()
𝟘 𝟙 ω 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 𝟙 ≤ω ()
𝟘 𝟙 ω 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 ω 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 ω 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 ω 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 ω 𝟘 ≤ω ≤ω ()
𝟘 𝟙 ω 𝟙 𝟘 𝟘 ()
𝟘 𝟙 ω 𝟙 𝟘 𝟙 ()
𝟘 𝟙 ω 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 𝟘 ≤ω ()
𝟘 𝟙 ω 𝟙 𝟙 𝟘 ()
𝟘 𝟙 ω 𝟙 𝟙 𝟙 ()
𝟘 𝟙 ω 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 𝟙 ≤ω ()
𝟘 𝟙 ω 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 ω 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 ω 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 ω 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 ω 𝟙 ≤ω ≤ω ()
𝟘 𝟙 ω ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 ω ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 ω ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 ω ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 ω ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 ω ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 ω ≤ω 𝟘 𝟘 ()
𝟘 𝟙 ω ≤ω 𝟘 𝟙 ()
𝟘 𝟙 ω ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 ω ≤ω 𝟘 ≤ω ()
𝟘 𝟙 ω ≤ω 𝟙 𝟘 ()
𝟘 𝟙 ω ≤ω 𝟙 𝟙 ()
𝟘 𝟙 ω ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤ω 𝟙 ≤ω ()
𝟘 𝟙 ω ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 ω ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 ω ≤ω ≤ω 𝟘 ()
𝟘 𝟙 ω ≤ω ≤ω 𝟙 ()
𝟘 𝟙 ω ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 ω ≤ω ≤ω ≤ω ()
𝟘 ω 𝟘 𝟘 𝟘 𝟙 ()
𝟘 ω 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 𝟘 ≤ω ()
𝟘 ω 𝟘 𝟘 𝟙 𝟘 ()
𝟘 ω 𝟘 𝟘 𝟙 𝟙 ()
𝟘 ω 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 𝟙 ≤ω ()
𝟘 ω 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 ω 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 ω 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 𝟘 ≤ω ≤ω ()
𝟘 ω 𝟘 𝟙 𝟘 𝟘 ()
𝟘 ω 𝟘 𝟙 𝟘 𝟙 ()
𝟘 ω 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 𝟘 ≤ω ()
𝟘 ω 𝟘 𝟙 𝟙 𝟘 ()
𝟘 ω 𝟘 𝟙 𝟙 𝟙 ()
𝟘 ω 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 𝟙 ≤ω ()
𝟘 ω 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 𝟙 ≤ω ≤ω ()
𝟘 ω 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 ω 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 ω 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 ω 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 ω 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 ω 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 ω 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 ω 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 ω 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 ω 𝟘 ≤ω ≤ω ≤ω ()
𝟘 ω 𝟙 𝟘 𝟘 𝟙 ()
𝟘 ω 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 𝟘 ≤ω ()
𝟘 ω 𝟙 𝟘 𝟙 𝟘 ()
𝟘 ω 𝟙 𝟘 𝟙 𝟙 ()
𝟘 ω 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 𝟙 ≤ω ()
𝟘 ω 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 ω 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 ω 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 𝟘 ≤ω ≤ω ()
𝟘 ω 𝟙 𝟙 𝟘 𝟘 ()
𝟘 ω 𝟙 𝟙 𝟘 𝟙 ()
𝟘 ω 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 𝟘 ≤ω ()
𝟘 ω 𝟙 𝟙 𝟙 𝟘 ()
𝟘 ω 𝟙 𝟙 𝟙 𝟙 ()
𝟘 ω 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 𝟙 ≤ω ()
𝟘 ω 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 𝟙 ≤ω ≤ω ()
𝟘 ω 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 ω 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 ω 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 ω 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 ω 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 ω 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 ω 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 ω 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 ω 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 ω 𝟙 ≤ω ≤ω ≤ω ()
𝟘 ω ω 𝟘 𝟘 𝟙 ()
𝟘 ω ω 𝟘 𝟘 ≤𝟙 ()
𝟘 ω ω 𝟘 𝟘 ≤ω ()
𝟘 ω ω 𝟘 𝟙 𝟘 ()
𝟘 ω ω 𝟘 𝟙 𝟙 ()
𝟘 ω ω 𝟘 𝟙 ≤𝟙 ()
𝟘 ω ω 𝟘 𝟙 ≤ω ()
𝟘 ω ω 𝟘 ≤𝟙 𝟘 ()
𝟘 ω ω 𝟘 ≤𝟙 𝟙 ()
𝟘 ω ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω ω 𝟘 ≤𝟙 ≤ω ()
𝟘 ω ω 𝟘 ≤ω 𝟘 ()
𝟘 ω ω 𝟘 ≤ω 𝟙 ()
𝟘 ω ω 𝟘 ≤ω ≤𝟙 ()
𝟘 ω ω 𝟘 ≤ω ≤ω ()
𝟘 ω ω 𝟙 𝟘 𝟘 ()
𝟘 ω ω 𝟙 𝟘 𝟙 ()
𝟘 ω ω 𝟙 𝟘 ≤𝟙 ()
𝟘 ω ω 𝟙 𝟘 ≤ω ()
𝟘 ω ω 𝟙 𝟙 𝟘 ()
𝟘 ω ω 𝟙 𝟙 𝟙 ()
𝟘 ω ω 𝟙 𝟙 ≤𝟙 ()
𝟘 ω ω 𝟙 𝟙 ≤ω ()
𝟘 ω ω 𝟙 ≤𝟙 𝟘 ()
𝟘 ω ω 𝟙 ≤𝟙 𝟙 ()
𝟘 ω ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω ω 𝟙 ≤𝟙 ≤ω ()
𝟘 ω ω 𝟙 ≤ω 𝟘 ()
𝟘 ω ω 𝟙 ≤ω 𝟙 ()
𝟘 ω ω 𝟙 ≤ω ≤𝟙 ()
𝟘 ω ω 𝟙 ≤ω ≤ω ()
𝟘 ω ω ≤𝟙 𝟘 𝟘 ()
𝟘 ω ω ≤𝟙 𝟘 𝟙 ()
𝟘 ω ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω ω ≤𝟙 𝟘 ≤ω ()
𝟘 ω ω ≤𝟙 𝟙 𝟘 ()
𝟘 ω ω ≤𝟙 𝟙 𝟙 ()
𝟘 ω ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω ω ≤𝟙 𝟙 ≤ω ()
𝟘 ω ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω ω ≤𝟙 ≤ω 𝟘 ()
𝟘 ω ω ≤𝟙 ≤ω 𝟙 ()
𝟘 ω ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω ω ≤𝟙 ≤ω ≤ω ()
𝟘 ω ω ≤ω 𝟘 𝟘 ()
𝟘 ω ω ≤ω 𝟘 𝟙 ()
𝟘 ω ω ≤ω 𝟘 ≤𝟙 ()
𝟘 ω ω ≤ω 𝟘 ≤ω ()
𝟘 ω ω ≤ω 𝟙 𝟘 ()
𝟘 ω ω ≤ω 𝟙 𝟙 ()
𝟘 ω ω ≤ω 𝟙 ≤𝟙 ()
𝟘 ω ω ≤ω 𝟙 ≤ω ()
𝟘 ω ω ≤ω ≤𝟙 𝟘 ()
𝟘 ω ω ≤ω ≤𝟙 𝟙 ()
𝟘 ω ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω ω ≤ω ≤𝟙 ≤ω ()
𝟘 ω ω ≤ω ≤ω 𝟘 ()
𝟘 ω ω ≤ω ≤ω 𝟙 ()
𝟘 ω ω ≤ω ≤ω ≤𝟙 ()
𝟘 ω ω ≤ω ≤ω ≤ω ()
𝟙 𝟘 𝟘 𝟘 𝟘 𝟘 ()
𝟙 𝟘 𝟘 𝟘 𝟘 𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟘 ≤ω ()
𝟙 𝟘 𝟘 𝟘 𝟙 𝟘 ()
𝟙 𝟘 𝟘 𝟘 𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤ω ≤ω ()
𝟙 𝟘 𝟘 𝟙 𝟘 𝟘 ()
𝟙 𝟘 𝟘 𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟘 𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 𝟘 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 𝟘 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤ω ≤ω ()
𝟙 𝟘 𝟙 𝟘 𝟘 𝟘 ()
𝟙 𝟘 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 𝟘 ≤ω ()
𝟙 𝟘 𝟙 𝟘 𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟘 𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤ω ≤ω ()
𝟙 𝟘 𝟙 𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟙 𝟙 𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 𝟘 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 𝟘 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤ω ≤ω ()
𝟙 𝟘 ω 𝟘 𝟘 𝟘 ()
𝟙 𝟘 ω 𝟘 𝟘 𝟙 ()
𝟙 𝟘 ω 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 𝟘 ≤ω ()
𝟙 𝟘 ω 𝟘 𝟙 𝟘 ()
𝟙 𝟘 ω 𝟘 𝟙 𝟙 ()
𝟙 𝟘 ω 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 𝟙 ≤ω ()
𝟙 𝟘 ω 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 ω 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 ω 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 ω 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 ω 𝟘 ≤ω ≤ω ()
𝟙 𝟘 ω 𝟙 𝟘 𝟘 ()
𝟙 𝟘 ω 𝟙 𝟘 𝟙 ()
𝟙 𝟘 ω 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 𝟘 ≤ω ()
𝟙 𝟘 ω 𝟙 𝟙 𝟘 ()
𝟙 𝟘 ω 𝟙 𝟙 𝟙 ()
𝟙 𝟘 ω 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 𝟙 ≤ω ()
𝟙 𝟘 ω 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 ω 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 ω 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 ω 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 ω 𝟙 ≤ω ≤ω ()
𝟙 𝟘 ω ≤𝟙 𝟘 𝟘 ()
𝟙 𝟘 ω ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 ω ≤𝟙 𝟙 𝟘 ()
𝟙 𝟘 ω ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 ω ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 ω ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 ω ≤ω 𝟘 𝟘 ()
𝟙 𝟘 ω ≤ω 𝟘 𝟙 ()
𝟙 𝟘 ω ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 ω ≤ω 𝟘 ≤ω ()
𝟙 𝟘 ω ≤ω 𝟙 𝟘 ()
𝟙 𝟘 ω ≤ω 𝟙 𝟙 ()
𝟙 𝟘 ω ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤ω 𝟙 ≤ω ()
𝟙 𝟘 ω ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 ω ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 ω ≤ω ≤ω 𝟘 ()
𝟙 𝟘 ω ≤ω ≤ω 𝟙 ()
𝟙 𝟘 ω ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 ω ≤ω ≤ω ≤ω ()
𝟙 𝟙 𝟘 𝟘 𝟘 𝟘 ()
𝟙 𝟙 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 𝟘 ≤ω ()
𝟙 𝟙 𝟘 𝟘 𝟙 𝟘 ()
𝟙 𝟙 𝟘 𝟘 𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤ω ≤ω ()
𝟙 𝟙 𝟘 𝟙 𝟘 𝟘 ()
𝟙 𝟙 𝟘 𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟘 𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 𝟙 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 𝟙 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤ω ≤ω ()
𝟙 𝟙 𝟙 𝟘 𝟘 𝟘 ()
𝟙 𝟙 𝟙 𝟘 𝟘 𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟘 ≤ω ()
𝟙 𝟙 𝟙 𝟘 𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟘 𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤ω ≤ω ()
𝟙 𝟙 𝟙 𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟙 𝟙 𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 𝟙 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 𝟙 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤ω ≤ω ()
𝟙 𝟙 ω 𝟘 𝟘 𝟘 ()
𝟙 𝟙 ω 𝟘 𝟘 𝟙 ()
𝟙 𝟙 ω 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 𝟘 ≤ω ()
𝟙 𝟙 ω 𝟘 𝟙 𝟘 ()
𝟙 𝟙 ω 𝟘 𝟙 𝟙 ()
𝟙 𝟙 ω 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 𝟙 ≤ω ()
𝟙 𝟙 ω 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 ω 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 ω 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 ω 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 ω 𝟘 ≤ω ≤ω ()
𝟙 𝟙 ω 𝟙 𝟘 𝟘 ()
𝟙 𝟙 ω 𝟙 𝟘 𝟙 ()
𝟙 𝟙 ω 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 𝟘 ≤ω ()
𝟙 𝟙 ω 𝟙 𝟙 𝟘 ()
𝟙 𝟙 ω 𝟙 𝟙 𝟙 ()
𝟙 𝟙 ω 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 𝟙 ≤ω ()
𝟙 𝟙 ω 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 ω 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 ω 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 ω 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 ω 𝟙 ≤ω ≤ω ()
𝟙 𝟙 ω ≤𝟙 𝟘 𝟘 ()
𝟙 𝟙 ω ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 ω ≤𝟙 𝟙 𝟘 ()
𝟙 𝟙 ω ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 ω ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 ω ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 ω ≤ω 𝟘 𝟘 ()
𝟙 𝟙 ω ≤ω 𝟘 𝟙 ()
𝟙 𝟙 ω ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 ω ≤ω 𝟘 ≤ω ()
𝟙 𝟙 ω ≤ω 𝟙 𝟘 ()
𝟙 𝟙 ω ≤ω 𝟙 𝟙 ()
𝟙 𝟙 ω ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤ω 𝟙 ≤ω ()
𝟙 𝟙 ω ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 ω ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 ω ≤ω ≤ω 𝟘 ()
𝟙 𝟙 ω ≤ω ≤ω 𝟙 ()
𝟙 𝟙 ω ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 ω ≤ω ≤ω ≤ω ()
𝟙 ω 𝟘 𝟘 𝟘 𝟘 ()
𝟙 ω 𝟘 𝟘 𝟘 𝟙 ()
𝟙 ω 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 𝟘 ≤ω ()
𝟙 ω 𝟘 𝟘 𝟙 𝟘 ()
𝟙 ω 𝟘 𝟘 𝟙 𝟙 ()
𝟙 ω 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 𝟙 ≤ω ()
𝟙 ω 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟙 ω 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 ω 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 ω 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 𝟘 ≤ω ≤ω ()
𝟙 ω 𝟘 𝟙 𝟘 𝟘 ()
𝟙 ω 𝟘 𝟙 𝟘 𝟙 ()
𝟙 ω 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 𝟘 ≤ω ()
𝟙 ω 𝟘 𝟙 𝟙 𝟙 ()
𝟙 ω 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 𝟙 ≤ω ()
𝟙 ω 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 𝟙 ≤ω ≤ω ()
𝟙 ω 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟙 ω 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟙 ω 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 ω 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 ω 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 ω 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 ω 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 ω 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 ω 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 ω 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 ω 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 ω 𝟘 ≤ω ≤ω ≤ω ()
𝟙 ω 𝟙 𝟘 𝟘 𝟘 ()
𝟙 ω 𝟙 𝟘 𝟘 𝟙 ()
𝟙 ω 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 𝟘 ≤ω ()
𝟙 ω 𝟙 𝟘 𝟙 𝟘 ()
𝟙 ω 𝟙 𝟘 𝟙 𝟙 ()
𝟙 ω 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 𝟙 ≤ω ()
𝟙 ω 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 ω 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 ω 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 𝟘 ≤ω ≤ω ()
𝟙 ω 𝟙 𝟙 𝟘 𝟙 ()
𝟙 ω 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 𝟘 ≤ω ()
𝟙 ω 𝟙 𝟙 𝟙 𝟘 ()
𝟙 ω 𝟙 𝟙 𝟙 𝟙 ()
𝟙 ω 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 𝟙 ≤ω ()
𝟙 ω 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 𝟙 ≤ω ≤ω ()
𝟙 ω 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 ω 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 ω 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 ω 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 ω 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 ω 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 ω 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 ω 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 ω 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 ω 𝟙 ≤ω ≤ω ≤ω ()
𝟙 ω ω 𝟘 𝟘 𝟘 ()
𝟙 ω ω 𝟘 𝟘 𝟙 ()
𝟙 ω ω 𝟘 𝟘 ≤𝟙 ()
𝟙 ω ω 𝟘 𝟘 ≤ω ()
𝟙 ω ω 𝟘 𝟙 𝟘 ()
𝟙 ω ω 𝟘 𝟙 𝟙 ()
𝟙 ω ω 𝟘 𝟙 ≤𝟙 ()
𝟙 ω ω 𝟘 𝟙 ≤ω ()
𝟙 ω ω 𝟘 ≤𝟙 𝟘 ()
𝟙 ω ω 𝟘 ≤𝟙 𝟙 ()
𝟙 ω ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω ω 𝟘 ≤𝟙 ≤ω ()
𝟙 ω ω 𝟘 ≤ω 𝟘 ()
𝟙 ω ω 𝟘 ≤ω 𝟙 ()
𝟙 ω ω 𝟘 ≤ω ≤𝟙 ()
𝟙 ω ω 𝟘 ≤ω ≤ω ()
𝟙 ω ω 𝟙 𝟘 𝟘 ()
𝟙 ω ω 𝟙 𝟘 𝟙 ()
𝟙 ω ω 𝟙 𝟘 ≤𝟙 ()
𝟙 ω ω 𝟙 𝟘 ≤ω ()
𝟙 ω ω 𝟙 𝟙 𝟘 ()
𝟙 ω ω 𝟙 𝟙 𝟙 ()
𝟙 ω ω 𝟙 𝟙 ≤𝟙 ()
𝟙 ω ω 𝟙 𝟙 ≤ω ()
𝟙 ω ω 𝟙 ≤𝟙 𝟘 ()
𝟙 ω ω 𝟙 ≤𝟙 𝟙 ()
𝟙 ω ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω ω 𝟙 ≤𝟙 ≤ω ()
𝟙 ω ω 𝟙 ≤ω 𝟘 ()
𝟙 ω ω 𝟙 ≤ω 𝟙 ()
𝟙 ω ω 𝟙 ≤ω ≤𝟙 ()
𝟙 ω ω 𝟙 ≤ω ≤ω ()
𝟙 ω ω ≤𝟙 𝟘 𝟘 ()
𝟙 ω ω ≤𝟙 𝟘 𝟙 ()
𝟙 ω ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω ω ≤𝟙 𝟘 ≤ω ()
𝟙 ω ω ≤𝟙 𝟙 𝟘 ()
𝟙 ω ω ≤𝟙 𝟙 𝟙 ()
𝟙 ω ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω ω ≤𝟙 𝟙 ≤ω ()
𝟙 ω ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 ω ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω ω ≤𝟙 ≤ω 𝟘 ()
𝟙 ω ω ≤𝟙 ≤ω 𝟙 ()
𝟙 ω ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω ω ≤𝟙 ≤ω ≤ω ()
𝟙 ω ω ≤ω 𝟘 𝟘 ()
𝟙 ω ω ≤ω 𝟘 𝟙 ()
𝟙 ω ω ≤ω 𝟘 ≤𝟙 ()
𝟙 ω ω ≤ω 𝟘 ≤ω ()
𝟙 ω ω ≤ω 𝟙 𝟘 ()
𝟙 ω ω ≤ω 𝟙 𝟙 ()
𝟙 ω ω ≤ω 𝟙 ≤𝟙 ()
𝟙 ω ω ≤ω 𝟙 ≤ω ()
𝟙 ω ω ≤ω ≤𝟙 𝟘 ()
𝟙 ω ω ≤ω ≤𝟙 𝟙 ()
𝟙 ω ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω ω ≤ω ≤𝟙 ≤ω ()
𝟙 ω ω ≤ω ≤ω 𝟘 ()
𝟙 ω ω ≤ω ≤ω 𝟙 ()
𝟙 ω ω ≤ω ≤ω ≤𝟙 ()
𝟙 ω ω ≤ω ≤ω ≤ω ()
opaque
linearity⇨linear-or-affine-no-nr-reflecting :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-reflecting-morphism
(linearityModality v₁)
(linear-or-affine v₂)
linearity→linear-or-affine
linearity⇨linear-or-affine-no-nr-reflecting {v₁} {v₂ = v₂@record{}} refl = λ where
.tr-≤-no-nr {s} → tr-≤-no-nr′ s
where
open Is-no-nr-reflecting-morphism
open Graded.Modality.Properties (linearityModality v₁)
tr : Linearity → Linear-or-affine
tr = linearity→linear-or-affine
tr⁻¹ : Linear-or-affine → Linearity
tr⁻¹ = linear-or-affine→linearity
tr⁻¹-monotone : ∀ p q → p LA.≤ q → tr⁻¹ p L.≤ tr⁻¹ q
tr⁻¹-monotone = λ where
𝟘 𝟘 refl → refl
𝟙 𝟙 refl → refl
≤𝟙 𝟘 refl → refl
≤𝟙 𝟙 refl → refl
≤𝟙 ≤𝟙 refl → refl
≤ω _ _ → refl
𝟘 𝟙 ()
𝟘 ≤𝟙 ()
𝟘 ≤ω ()
𝟙 𝟘 ()
𝟙 ≤𝟙 ()
𝟙 ≤ω ()
≤𝟙 ≤ω ()
tr-tr⁻¹≤ : ∀ p → tr (tr⁻¹ p) LA.≤ p
tr-tr⁻¹≤ = λ where
𝟘 → refl
𝟙 → refl
≤𝟙 → refl
≤ω → refl
tr≤→≤tr⁻¹ : ∀ p q → tr p LA.≤ q → p L.≤ tr⁻¹ q
tr≤→≤tr⁻¹ = λ where
𝟘 𝟘 refl → refl
𝟙 𝟙 refl → refl
ω _ _ → refl
𝟘 𝟙 ()
𝟘 ≤𝟙 ()
𝟘 ≤ω ()
𝟙 𝟘 ()
𝟙 ≤𝟙 ()
𝟙 ≤ω ()
tr⁻¹-∧ : ∀ p q → tr⁻¹ (p LA.∧ q) ≡ tr⁻¹ p L.∧ tr⁻¹ q
tr⁻¹-∧ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
≤𝟙 𝟘 → refl
≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω → refl
≤ω _ → refl
tr⁻¹-+ : ∀ p q → tr⁻¹ (p LA.+ q) ≡ tr⁻¹ p L.+ tr⁻¹ q
tr⁻¹-+ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
≤𝟙 𝟘 → refl
≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω → refl
≤ω 𝟘 → refl
≤ω 𝟙 → refl
≤ω ≤𝟙 → refl
≤ω ≤ω → refl
tr⁻¹-· : ∀ p q → tr⁻¹ (tr p LA.· q) ≡ p L.· tr⁻¹ q
tr⁻¹-· = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
ω 𝟘 → refl
ω 𝟙 → refl
ω ≤𝟙 → refl
ω ≤ω → refl
tr-≤-no-nr′ :
∀ s →
tr p LA.≤ q₁ →
q₁ LA.≤ q₂ →
(T (Modality-variant.𝟘ᵐ-allowed v₁) →
q₁ LA.≤ q₃) →
(⦃ 𝟘-well-behaved :
Has-well-behaved-zero Linear-or-affine
LA.linear-or-affine-semiring-with-meet ⦄ →
q₁ LA.≤ q₄) →
q₁ LA.≤ q₃ LA.+ tr r LA.· q₄ LA.+ tr s LA.· q₁ →
∃₄ λ q₁′ q₂′ q₃′ q₄′ →
tr q₂′ LA.≤ q₂ ×
tr q₃′ LA.≤ q₃ ×
tr q₄′ LA.≤ q₄ ×
p L.≤ q₁′ ×
q₁′ L.≤ q₂′ ×
(T (Modality-variant.𝟘ᵐ-allowed v₂) →
q₁′ L.≤ q₃′) ×
(⦃ 𝟘-well-behaved :
Has-well-behaved-zero Linearity
(Modality.semiring-with-meet (linearityModality v₂)) ⦄ →
q₁′ L.≤ q₄′) ×
q₁′ L.≤ q₃′ L.+ r L.· q₄′ L.+ s L.· q₁′
tr-≤-no-nr′ s = →tr-≤-no-nr {s = s}
(linearityModality v₁)
(linear-or-affine v₂)
idᶠ
LA.linear-or-affine-has-well-behaved-zero
tr
tr⁻¹
tr⁻¹-monotone
tr≤→≤tr⁻¹
tr-tr⁻¹≤
(λ p q → ≤-reflexive (tr⁻¹-+ p q))
(λ p q → ≤-reflexive (tr⁻¹-∧ p q))
(λ p q → ≤-reflexive (tr⁻¹-· p q))
opaque
affine⇨linear-or-affine-nr-reflecting :
Is-nr-reflecting-morphism
(affineModality v₁)
(linear-or-affine v₂)
⦃ A.zero-one-many-has-nr ⦄
⦃ LA.linear-or-affine-has-nr ⦄
affine→linear-or-affine
affine⇨linear-or-affine-nr-reflecting = λ where
.tr-≤-nr {r} → tr-≤-nr′ _ _ r _ _ _
where
open Is-nr-reflecting-morphism
tr : Affine → Linear-or-affine
tr = affine→linear-or-affine
tr-≤-nr′ :
∀ q p r z₁ s₁ n₁ →
tr q LA.≤ LA.nr (tr p) (tr r) z₁ s₁ n₁ →
∃₃ λ z₂ s₂ n₂ →
tr z₂ LA.≤ z₁ × tr s₂ LA.≤ s₁ × tr n₂ LA.≤ n₁ ×
q A.≤ A.nr p r z₂ s₂ n₂
tr-≤-nr′ = λ where
ω _ _ _ _ _ _ → ω , ω , ω , refl , refl , refl , refl
𝟘 𝟘 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟙 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω 𝟙 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 ω ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟘 𝟘 𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟘 𝟘 ≤𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟘 𝟙 𝟘 _ → 𝟘 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟘 ≤𝟙 𝟘 _ → 𝟘 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 ≤𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟘 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟘 𝟘 𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟘 𝟘 ≤𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟘 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 𝟙 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟘 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 𝟘 𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 𝟘 ≤𝟙 _ → 𝟘 , 𝟘 , 𝟙 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟘 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 ≤𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟙 𝟘 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 𝟙 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 𝟙 ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟘 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟘 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟘 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 ≤𝟙 𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 𝟘 _ → 𝟙 , 𝟙 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟙 𝟘 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟙 𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω 𝟙 ≤𝟙 𝟘 𝟘 _ → 𝟙 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟙 ω ω 𝟘 𝟘 𝟘 _ → 𝟘 , 𝟘 , 𝟘 , refl , refl , refl , refl
𝟘 𝟘 𝟘 𝟘 𝟘 𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟘 ≤ω ()
𝟘 𝟘 𝟘 𝟘 𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟘 𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 𝟘 ≤ω ≤ω ()
𝟘 𝟘 𝟘 𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟘 𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟘 𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 𝟘 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 𝟘 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 𝟘 ≤ω ≤ω ≤ω ()
𝟘 𝟘 𝟙 𝟘 𝟘 𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟘 ≤ω ()
𝟘 𝟘 𝟙 𝟘 𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟘 𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 𝟘 ≤ω ≤ω ()
𝟘 𝟘 𝟙 𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟙 𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟙 𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 𝟘 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 𝟘 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 𝟙 ≤ω ≤ω ≤ω ()
𝟘 𝟘 ω 𝟘 𝟘 𝟙 ()
𝟘 𝟘 ω 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 𝟘 ≤ω ()
𝟘 𝟘 ω 𝟘 𝟙 𝟘 ()
𝟘 𝟘 ω 𝟘 𝟙 𝟙 ()
𝟘 𝟘 ω 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 𝟙 ≤ω ()
𝟘 𝟘 ω 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟘 ω 𝟘 ≤ω 𝟘 ()
𝟘 𝟘 ω 𝟘 ≤ω 𝟙 ()
𝟘 𝟘 ω 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟘 ω 𝟘 ≤ω ≤ω ()
𝟘 𝟘 ω 𝟙 𝟘 𝟘 ()
𝟘 𝟘 ω 𝟙 𝟘 𝟙 ()
𝟘 𝟘 ω 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 𝟘 ≤ω ()
𝟘 𝟘 ω 𝟙 𝟙 𝟘 ()
𝟘 𝟘 ω 𝟙 𝟙 𝟙 ()
𝟘 𝟘 ω 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 𝟙 ≤ω ()
𝟘 𝟘 ω 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 ω 𝟙 ≤ω 𝟘 ()
𝟘 𝟘 ω 𝟙 ≤ω 𝟙 ()
𝟘 𝟘 ω 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 ω 𝟙 ≤ω ≤ω ()
𝟘 𝟘 ω ≤𝟙 𝟘 𝟘 ()
𝟘 𝟘 ω ≤𝟙 𝟘 𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟘 ≤ω ()
𝟘 𝟘 ω ≤𝟙 𝟙 𝟘 ()
𝟘 𝟘 ω ≤𝟙 𝟙 𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 𝟙 ≤ω ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟘 ω ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟘 ω ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟘 ω ≤𝟙 ≤ω ≤ω ()
𝟘 𝟘 ω ≤ω 𝟘 𝟘 ()
𝟘 𝟘 ω ≤ω 𝟘 𝟙 ()
𝟘 𝟘 ω ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟘 ω ≤ω 𝟘 ≤ω ()
𝟘 𝟘 ω ≤ω 𝟙 𝟘 ()
𝟘 𝟘 ω ≤ω 𝟙 𝟙 ()
𝟘 𝟘 ω ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤ω 𝟙 ≤ω ()
𝟘 𝟘 ω ≤ω ≤𝟙 𝟘 ()
𝟘 𝟘 ω ≤ω ≤𝟙 𝟙 ()
𝟘 𝟘 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟘 ω ≤ω ≤𝟙 ≤ω ()
𝟘 𝟘 ω ≤ω ≤ω 𝟘 ()
𝟘 𝟘 ω ≤ω ≤ω 𝟙 ()
𝟘 𝟘 ω ≤ω ≤ω ≤𝟙 ()
𝟘 𝟘 ω ≤ω ≤ω ≤ω ()
𝟘 𝟙 𝟘 𝟘 𝟘 𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟘 ≤ω ()
𝟘 𝟙 𝟘 𝟘 𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟘 𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 𝟘 ≤ω ≤ω ()
𝟘 𝟙 𝟘 𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟘 𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟘 𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 𝟙 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 𝟙 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 𝟘 ≤ω ≤ω ≤ω ()
𝟘 𝟙 𝟙 𝟘 𝟘 𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟘 ≤ω ()
𝟘 𝟙 𝟙 𝟘 𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟘 𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 𝟘 ≤ω ≤ω ()
𝟘 𝟙 𝟙 𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟙 𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟙 𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 𝟙 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 𝟙 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 𝟙 ≤ω ≤ω ≤ω ()
𝟘 𝟙 ω 𝟘 𝟘 𝟙 ()
𝟘 𝟙 ω 𝟘 𝟘 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 𝟘 ≤ω ()
𝟘 𝟙 ω 𝟘 𝟙 𝟘 ()
𝟘 𝟙 ω 𝟘 𝟙 𝟙 ()
𝟘 𝟙 ω 𝟘 𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 𝟙 ≤ω ()
𝟘 𝟙 ω 𝟘 ≤𝟙 𝟘 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 𝟙 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟘 ≤𝟙 ≤ω ()
𝟘 𝟙 ω 𝟘 ≤ω 𝟘 ()
𝟘 𝟙 ω 𝟘 ≤ω 𝟙 ()
𝟘 𝟙 ω 𝟘 ≤ω ≤𝟙 ()
𝟘 𝟙 ω 𝟘 ≤ω ≤ω ()
𝟘 𝟙 ω 𝟙 𝟘 𝟘 ()
𝟘 𝟙 ω 𝟙 𝟘 𝟙 ()
𝟘 𝟙 ω 𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 𝟘 ≤ω ()
𝟘 𝟙 ω 𝟙 𝟙 𝟘 ()
𝟘 𝟙 ω 𝟙 𝟙 𝟙 ()
𝟘 𝟙 ω 𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 𝟙 ≤ω ()
𝟘 𝟙 ω 𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω 𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 ω 𝟙 ≤ω 𝟘 ()
𝟘 𝟙 ω 𝟙 ≤ω 𝟙 ()
𝟘 𝟙 ω 𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 ω 𝟙 ≤ω ≤ω ()
𝟘 𝟙 ω ≤𝟙 𝟘 𝟘 ()
𝟘 𝟙 ω ≤𝟙 𝟘 𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟘 ≤ω ()
𝟘 𝟙 ω ≤𝟙 𝟙 𝟘 ()
𝟘 𝟙 ω ≤𝟙 𝟙 𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 𝟙 ≤ω ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 𝟙 ω ≤𝟙 ≤ω 𝟘 ()
𝟘 𝟙 ω ≤𝟙 ≤ω 𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 𝟙 ω ≤𝟙 ≤ω ≤ω ()
𝟘 𝟙 ω ≤ω 𝟘 𝟘 ()
𝟘 𝟙 ω ≤ω 𝟘 𝟙 ()
𝟘 𝟙 ω ≤ω 𝟘 ≤𝟙 ()
𝟘 𝟙 ω ≤ω 𝟘 ≤ω ()
𝟘 𝟙 ω ≤ω 𝟙 𝟘 ()
𝟘 𝟙 ω ≤ω 𝟙 𝟙 ()
𝟘 𝟙 ω ≤ω 𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤ω 𝟙 ≤ω ()
𝟘 𝟙 ω ≤ω ≤𝟙 𝟘 ()
𝟘 𝟙 ω ≤ω ≤𝟙 𝟙 ()
𝟘 𝟙 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 𝟙 ω ≤ω ≤𝟙 ≤ω ()
𝟘 𝟙 ω ≤ω ≤ω 𝟘 ()
𝟘 𝟙 ω ≤ω ≤ω 𝟙 ()
𝟘 𝟙 ω ≤ω ≤ω ≤𝟙 ()
𝟘 𝟙 ω ≤ω ≤ω ≤ω ()
𝟘 ω 𝟘 𝟘 𝟘 𝟙 ()
𝟘 ω 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 𝟘 ≤ω ()
𝟘 ω 𝟘 𝟘 𝟙 𝟘 ()
𝟘 ω 𝟘 𝟘 𝟙 𝟙 ()
𝟘 ω 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 𝟙 ≤ω ()
𝟘 ω 𝟘 𝟘 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 𝟘 ≤ω 𝟘 ()
𝟘 ω 𝟘 𝟘 ≤ω 𝟙 ()
𝟘 ω 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 𝟘 ≤ω ≤ω ()
𝟘 ω 𝟘 𝟙 𝟘 𝟘 ()
𝟘 ω 𝟘 𝟙 𝟘 𝟙 ()
𝟘 ω 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 𝟘 ≤ω ()
𝟘 ω 𝟘 𝟙 𝟙 𝟘 ()
𝟘 ω 𝟘 𝟙 𝟙 𝟙 ()
𝟘 ω 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 𝟙 ≤ω ()
𝟘 ω 𝟘 𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟘 𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 𝟙 ≤ω ≤ω ()
𝟘 ω 𝟘 ≤𝟙 𝟘 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 𝟙 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟘 ω 𝟘 ≤ω 𝟘 𝟘 ()
𝟘 ω 𝟘 ≤ω 𝟘 𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟘 ≤ω ()
𝟘 ω 𝟘 ≤ω 𝟙 𝟘 ()
𝟘 ω 𝟘 ≤ω 𝟙 𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω 𝟙 ≤ω ()
𝟘 ω 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟘 ω 𝟘 ≤ω ≤ω 𝟘 ()
𝟘 ω 𝟘 ≤ω ≤ω 𝟙 ()
𝟘 ω 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟘 ω 𝟘 ≤ω ≤ω ≤ω ()
𝟘 ω 𝟙 𝟘 𝟘 𝟙 ()
𝟘 ω 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 𝟘 ≤ω ()
𝟘 ω 𝟙 𝟘 𝟙 𝟘 ()
𝟘 ω 𝟙 𝟘 𝟙 𝟙 ()
𝟘 ω 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 𝟙 ≤ω ()
𝟘 ω 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 𝟘 ≤ω 𝟘 ()
𝟘 ω 𝟙 𝟘 ≤ω 𝟙 ()
𝟘 ω 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 𝟘 ≤ω ≤ω ()
𝟘 ω 𝟙 𝟙 𝟘 𝟘 ()
𝟘 ω 𝟙 𝟙 𝟘 𝟙 ()
𝟘 ω 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 𝟘 ≤ω ()
𝟘 ω 𝟙 𝟙 𝟙 𝟘 ()
𝟘 ω 𝟙 𝟙 𝟙 𝟙 ()
𝟘 ω 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 𝟙 ≤ω ()
𝟘 ω 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟙 𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 𝟙 ≤ω ≤ω ()
𝟘 ω 𝟙 ≤𝟙 𝟘 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟘 ω 𝟙 ≤ω 𝟘 𝟘 ()
𝟘 ω 𝟙 ≤ω 𝟘 𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟘 ≤ω ()
𝟘 ω 𝟙 ≤ω 𝟙 𝟘 ()
𝟘 ω 𝟙 ≤ω 𝟙 𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω 𝟙 ≤ω ()
𝟘 ω 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟘 ω 𝟙 ≤ω ≤ω 𝟘 ()
𝟘 ω 𝟙 ≤ω ≤ω 𝟙 ()
𝟘 ω 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟘 ω 𝟙 ≤ω ≤ω ≤ω ()
𝟘 ω ω 𝟘 𝟘 𝟙 ()
𝟘 ω ω 𝟘 𝟘 ≤𝟙 ()
𝟘 ω ω 𝟘 𝟘 ≤ω ()
𝟘 ω ω 𝟘 𝟙 𝟘 ()
𝟘 ω ω 𝟘 𝟙 𝟙 ()
𝟘 ω ω 𝟘 𝟙 ≤𝟙 ()
𝟘 ω ω 𝟘 𝟙 ≤ω ()
𝟘 ω ω 𝟘 ≤𝟙 𝟘 ()
𝟘 ω ω 𝟘 ≤𝟙 𝟙 ()
𝟘 ω ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟘 ω ω 𝟘 ≤𝟙 ≤ω ()
𝟘 ω ω 𝟘 ≤ω 𝟘 ()
𝟘 ω ω 𝟘 ≤ω 𝟙 ()
𝟘 ω ω 𝟘 ≤ω ≤𝟙 ()
𝟘 ω ω 𝟘 ≤ω ≤ω ()
𝟘 ω ω 𝟙 𝟘 𝟘 ()
𝟘 ω ω 𝟙 𝟘 𝟙 ()
𝟘 ω ω 𝟙 𝟘 ≤𝟙 ()
𝟘 ω ω 𝟙 𝟘 ≤ω ()
𝟘 ω ω 𝟙 𝟙 𝟘 ()
𝟘 ω ω 𝟙 𝟙 𝟙 ()
𝟘 ω ω 𝟙 𝟙 ≤𝟙 ()
𝟘 ω ω 𝟙 𝟙 ≤ω ()
𝟘 ω ω 𝟙 ≤𝟙 𝟘 ()
𝟘 ω ω 𝟙 ≤𝟙 𝟙 ()
𝟘 ω ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω ω 𝟙 ≤𝟙 ≤ω ()
𝟘 ω ω 𝟙 ≤ω 𝟘 ()
𝟘 ω ω 𝟙 ≤ω 𝟙 ()
𝟘 ω ω 𝟙 ≤ω ≤𝟙 ()
𝟘 ω ω 𝟙 ≤ω ≤ω ()
𝟘 ω ω ≤𝟙 𝟘 𝟘 ()
𝟘 ω ω ≤𝟙 𝟘 𝟙 ()
𝟘 ω ω ≤𝟙 𝟘 ≤𝟙 ()
𝟘 ω ω ≤𝟙 𝟘 ≤ω ()
𝟘 ω ω ≤𝟙 𝟙 𝟘 ()
𝟘 ω ω ≤𝟙 𝟙 𝟙 ()
𝟘 ω ω ≤𝟙 𝟙 ≤𝟙 ()
𝟘 ω ω ≤𝟙 𝟙 ≤ω ()
𝟘 ω ω ≤𝟙 ≤𝟙 𝟘 ()
𝟘 ω ω ≤𝟙 ≤𝟙 𝟙 ()
𝟘 ω ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟘 ω ω ≤𝟙 ≤𝟙 ≤ω ()
𝟘 ω ω ≤𝟙 ≤ω 𝟘 ()
𝟘 ω ω ≤𝟙 ≤ω 𝟙 ()
𝟘 ω ω ≤𝟙 ≤ω ≤𝟙 ()
𝟘 ω ω ≤𝟙 ≤ω ≤ω ()
𝟘 ω ω ≤ω 𝟘 𝟘 ()
𝟘 ω ω ≤ω 𝟘 𝟙 ()
𝟘 ω ω ≤ω 𝟘 ≤𝟙 ()
𝟘 ω ω ≤ω 𝟘 ≤ω ()
𝟘 ω ω ≤ω 𝟙 𝟘 ()
𝟘 ω ω ≤ω 𝟙 𝟙 ()
𝟘 ω ω ≤ω 𝟙 ≤𝟙 ()
𝟘 ω ω ≤ω 𝟙 ≤ω ()
𝟘 ω ω ≤ω ≤𝟙 𝟘 ()
𝟘 ω ω ≤ω ≤𝟙 𝟙 ()
𝟘 ω ω ≤ω ≤𝟙 ≤𝟙 ()
𝟘 ω ω ≤ω ≤𝟙 ≤ω ()
𝟘 ω ω ≤ω ≤ω 𝟘 ()
𝟘 ω ω ≤ω ≤ω 𝟙 ()
𝟘 ω ω ≤ω ≤ω ≤𝟙 ()
𝟘 ω ω ≤ω ≤ω ≤ω ()
𝟙 𝟘 𝟘 𝟘 𝟘 ≤ω ()
𝟙 𝟘 𝟘 𝟘 𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 𝟘 ≤ω ≤ω ()
𝟙 𝟘 𝟘 𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟘 𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 𝟘 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 𝟘 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 𝟘 ≤ω ≤ω ≤ω ()
𝟙 𝟘 𝟙 𝟘 𝟘 ≤ω ()
𝟙 𝟘 𝟙 𝟘 𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟘 𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 𝟘 ≤ω ≤ω ()
𝟙 𝟘 𝟙 𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟙 𝟙 𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 𝟘 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 𝟘 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 𝟙 ≤ω ≤ω ≤ω ()
𝟙 𝟘 ω 𝟘 𝟘 𝟙 ()
𝟙 𝟘 ω 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 𝟘 ≤ω ()
𝟙 𝟘 ω 𝟘 𝟙 𝟘 ()
𝟙 𝟘 ω 𝟘 𝟙 𝟙 ()
𝟙 𝟘 ω 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 𝟙 ≤ω ()
𝟙 𝟘 ω 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟘 ω 𝟘 ≤ω 𝟘 ()
𝟙 𝟘 ω 𝟘 ≤ω 𝟙 ()
𝟙 𝟘 ω 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟘 ω 𝟘 ≤ω ≤ω ()
𝟙 𝟘 ω 𝟙 𝟘 𝟘 ()
𝟙 𝟘 ω 𝟙 𝟘 𝟙 ()
𝟙 𝟘 ω 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 𝟘 ≤ω ()
𝟙 𝟘 ω 𝟙 𝟙 𝟘 ()
𝟙 𝟘 ω 𝟙 𝟙 𝟙 ()
𝟙 𝟘 ω 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 𝟙 ≤ω ()
𝟙 𝟘 ω 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 ω 𝟙 ≤ω 𝟘 ()
𝟙 𝟘 ω 𝟙 ≤ω 𝟙 ()
𝟙 𝟘 ω 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 ω 𝟙 ≤ω ≤ω ()
𝟙 𝟘 ω ≤𝟙 𝟘 𝟘 ()
𝟙 𝟘 ω ≤𝟙 𝟘 𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟘 ≤ω ()
𝟙 𝟘 ω ≤𝟙 𝟙 𝟘 ()
𝟙 𝟘 ω ≤𝟙 𝟙 𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 𝟙 ≤ω ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟘 ω ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟘 ω ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟘 ω ≤𝟙 ≤ω ≤ω ()
𝟙 𝟘 ω ≤ω 𝟘 𝟘 ()
𝟙 𝟘 ω ≤ω 𝟘 𝟙 ()
𝟙 𝟘 ω ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟘 ω ≤ω 𝟘 ≤ω ()
𝟙 𝟘 ω ≤ω 𝟙 𝟘 ()
𝟙 𝟘 ω ≤ω 𝟙 𝟙 ()
𝟙 𝟘 ω ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤ω 𝟙 ≤ω ()
𝟙 𝟘 ω ≤ω ≤𝟙 𝟘 ()
𝟙 𝟘 ω ≤ω ≤𝟙 𝟙 ()
𝟙 𝟘 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟘 ω ≤ω ≤𝟙 ≤ω ()
𝟙 𝟘 ω ≤ω ≤ω 𝟘 ()
𝟙 𝟘 ω ≤ω ≤ω 𝟙 ()
𝟙 𝟘 ω ≤ω ≤ω ≤𝟙 ()
𝟙 𝟘 ω ≤ω ≤ω ≤ω ()
𝟙 𝟙 𝟘 𝟘 𝟘 ≤ω ()
𝟙 𝟙 𝟘 𝟘 𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 𝟘 ≤ω ≤ω ()
𝟙 𝟙 𝟘 𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟘 𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 𝟙 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 𝟙 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 𝟘 ≤ω ≤ω ≤ω ()
𝟙 𝟙 𝟙 𝟘 𝟘 𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟘 ≤ω ()
𝟙 𝟙 𝟙 𝟘 𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟘 𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 𝟘 ≤ω ≤ω ()
𝟙 𝟙 𝟙 𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟙 𝟙 𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 𝟙 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 𝟙 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 𝟙 ≤ω ≤ω ≤ω ()
𝟙 𝟙 ω 𝟘 𝟘 𝟙 ()
𝟙 𝟙 ω 𝟘 𝟘 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 𝟘 ≤ω ()
𝟙 𝟙 ω 𝟘 𝟙 𝟘 ()
𝟙 𝟙 ω 𝟘 𝟙 𝟙 ()
𝟙 𝟙 ω 𝟘 𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 𝟙 ≤ω ()
𝟙 𝟙 ω 𝟘 ≤𝟙 𝟘 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 𝟙 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟘 ≤𝟙 ≤ω ()
𝟙 𝟙 ω 𝟘 ≤ω 𝟘 ()
𝟙 𝟙 ω 𝟘 ≤ω 𝟙 ()
𝟙 𝟙 ω 𝟘 ≤ω ≤𝟙 ()
𝟙 𝟙 ω 𝟘 ≤ω ≤ω ()
𝟙 𝟙 ω 𝟙 𝟘 𝟘 ()
𝟙 𝟙 ω 𝟙 𝟘 𝟙 ()
𝟙 𝟙 ω 𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 𝟘 ≤ω ()
𝟙 𝟙 ω 𝟙 𝟙 𝟘 ()
𝟙 𝟙 ω 𝟙 𝟙 𝟙 ()
𝟙 𝟙 ω 𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 𝟙 ≤ω ()
𝟙 𝟙 ω 𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω 𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 ω 𝟙 ≤ω 𝟘 ()
𝟙 𝟙 ω 𝟙 ≤ω 𝟙 ()
𝟙 𝟙 ω 𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 ω 𝟙 ≤ω ≤ω ()
𝟙 𝟙 ω ≤𝟙 𝟘 𝟘 ()
𝟙 𝟙 ω ≤𝟙 𝟘 𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟘 ≤ω ()
𝟙 𝟙 ω ≤𝟙 𝟙 𝟘 ()
𝟙 𝟙 ω ≤𝟙 𝟙 𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 𝟙 ≤ω ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 𝟙 ω ≤𝟙 ≤ω 𝟘 ()
𝟙 𝟙 ω ≤𝟙 ≤ω 𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 𝟙 ω ≤𝟙 ≤ω ≤ω ()
𝟙 𝟙 ω ≤ω 𝟘 𝟘 ()
𝟙 𝟙 ω ≤ω 𝟘 𝟙 ()
𝟙 𝟙 ω ≤ω 𝟘 ≤𝟙 ()
𝟙 𝟙 ω ≤ω 𝟘 ≤ω ()
𝟙 𝟙 ω ≤ω 𝟙 𝟘 ()
𝟙 𝟙 ω ≤ω 𝟙 𝟙 ()
𝟙 𝟙 ω ≤ω 𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤ω 𝟙 ≤ω ()
𝟙 𝟙 ω ≤ω ≤𝟙 𝟘 ()
𝟙 𝟙 ω ≤ω ≤𝟙 𝟙 ()
𝟙 𝟙 ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 𝟙 ω ≤ω ≤𝟙 ≤ω ()
𝟙 𝟙 ω ≤ω ≤ω 𝟘 ()
𝟙 𝟙 ω ≤ω ≤ω 𝟙 ()
𝟙 𝟙 ω ≤ω ≤ω ≤𝟙 ()
𝟙 𝟙 ω ≤ω ≤ω ≤ω ()
𝟙 ω 𝟘 𝟘 𝟘 𝟙 ()
𝟙 ω 𝟘 𝟘 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 𝟘 ≤ω ()
𝟙 ω 𝟘 𝟘 𝟙 𝟙 ()
𝟙 ω 𝟘 𝟘 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 𝟙 ≤ω ()
𝟙 ω 𝟘 𝟘 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟘 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 𝟘 ≤ω 𝟘 ()
𝟙 ω 𝟘 𝟘 ≤ω 𝟙 ()
𝟙 ω 𝟘 𝟘 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 𝟘 ≤ω ≤ω ()
𝟙 ω 𝟘 𝟙 𝟘 𝟙 ()
𝟙 ω 𝟘 𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 𝟘 ≤ω ()
𝟙 ω 𝟘 𝟙 𝟙 𝟙 ()
𝟙 ω 𝟘 𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 𝟙 ≤ω ()
𝟙 ω 𝟘 𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟘 𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟘 𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 𝟙 ≤ω ≤ω ()
𝟙 ω 𝟘 ≤𝟙 𝟘 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟘 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 𝟙 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 𝟙 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟘 ≤𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟘 ≤𝟙 ≤ω ≤ω ()
𝟙 ω 𝟘 ≤ω 𝟘 𝟘 ()
𝟙 ω 𝟘 ≤ω 𝟘 𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟘 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟘 ≤ω ()
𝟙 ω 𝟘 ≤ω 𝟙 𝟘 ()
𝟙 ω 𝟘 ≤ω 𝟙 𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω 𝟙 ≤ω ()
𝟙 ω 𝟘 ≤ω ≤𝟙 𝟘 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 𝟙 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟘 ≤ω ≤𝟙 ≤ω ()
𝟙 ω 𝟘 ≤ω ≤ω 𝟘 ()
𝟙 ω 𝟘 ≤ω ≤ω 𝟙 ()
𝟙 ω 𝟘 ≤ω ≤ω ≤𝟙 ()
𝟙 ω 𝟘 ≤ω ≤ω ≤ω ()
𝟙 ω 𝟙 𝟘 𝟘 𝟙 ()
𝟙 ω 𝟙 𝟘 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 𝟘 ≤ω ()
𝟙 ω 𝟙 𝟘 𝟙 𝟘 ()
𝟙 ω 𝟙 𝟘 𝟙 𝟙 ()
𝟙 ω 𝟙 𝟘 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 𝟙 ≤ω ()
𝟙 ω 𝟙 𝟘 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟘 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 𝟘 ≤ω 𝟘 ()
𝟙 ω 𝟙 𝟘 ≤ω 𝟙 ()
𝟙 ω 𝟙 𝟘 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 𝟘 ≤ω ≤ω ()
𝟙 ω 𝟙 𝟙 𝟘 𝟙 ()
𝟙 ω 𝟙 𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 𝟘 ≤ω ()
𝟙 ω 𝟙 𝟙 𝟙 𝟘 ()
𝟙 ω 𝟙 𝟙 𝟙 𝟙 ()
𝟙 ω 𝟙 𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 𝟙 ≤ω ()
𝟙 ω 𝟙 𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟙 𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟙 𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 𝟙 ≤ω ≤ω ()
𝟙 ω 𝟙 ≤𝟙 𝟘 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟘 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 𝟙 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 𝟙 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω 𝟙 ≤𝟙 ≤ω 𝟘 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω 𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω 𝟙 ≤𝟙 ≤ω ≤ω ()
𝟙 ω 𝟙 ≤ω 𝟘 𝟘 ()
𝟙 ω 𝟙 ≤ω 𝟘 𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟘 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟘 ≤ω ()
𝟙 ω 𝟙 ≤ω 𝟙 𝟘 ()
𝟙 ω 𝟙 ≤ω 𝟙 𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω 𝟙 ≤ω ()
𝟙 ω 𝟙 ≤ω ≤𝟙 𝟘 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 𝟙 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω 𝟙 ≤ω ≤𝟙 ≤ω ()
𝟙 ω 𝟙 ≤ω ≤ω 𝟘 ()
𝟙 ω 𝟙 ≤ω ≤ω 𝟙 ()
𝟙 ω 𝟙 ≤ω ≤ω ≤𝟙 ()
𝟙 ω 𝟙 ≤ω ≤ω ≤ω ()
𝟙 ω ω 𝟘 𝟘 𝟙 ()
𝟙 ω ω 𝟘 𝟘 ≤𝟙 ()
𝟙 ω ω 𝟘 𝟘 ≤ω ()
𝟙 ω ω 𝟘 𝟙 𝟘 ()
𝟙 ω ω 𝟘 𝟙 𝟙 ()
𝟙 ω ω 𝟘 𝟙 ≤𝟙 ()
𝟙 ω ω 𝟘 𝟙 ≤ω ()
𝟙 ω ω 𝟘 ≤𝟙 𝟘 ()
𝟙 ω ω 𝟘 ≤𝟙 𝟙 ()
𝟙 ω ω 𝟘 ≤𝟙 ≤𝟙 ()
𝟙 ω ω 𝟘 ≤𝟙 ≤ω ()
𝟙 ω ω 𝟘 ≤ω 𝟘 ()
𝟙 ω ω 𝟘 ≤ω 𝟙 ()
𝟙 ω ω 𝟘 ≤ω ≤𝟙 ()
𝟙 ω ω 𝟘 ≤ω ≤ω ()
𝟙 ω ω 𝟙 𝟘 𝟘 ()
𝟙 ω ω 𝟙 𝟘 𝟙 ()
𝟙 ω ω 𝟙 𝟘 ≤𝟙 ()
𝟙 ω ω 𝟙 𝟘 ≤ω ()
𝟙 ω ω 𝟙 𝟙 𝟘 ()
𝟙 ω ω 𝟙 𝟙 𝟙 ()
𝟙 ω ω 𝟙 𝟙 ≤𝟙 ()
𝟙 ω ω 𝟙 𝟙 ≤ω ()
𝟙 ω ω 𝟙 ≤𝟙 𝟘 ()
𝟙 ω ω 𝟙 ≤𝟙 𝟙 ()
𝟙 ω ω 𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω ω 𝟙 ≤𝟙 ≤ω ()
𝟙 ω ω 𝟙 ≤ω 𝟘 ()
𝟙 ω ω 𝟙 ≤ω 𝟙 ()
𝟙 ω ω 𝟙 ≤ω ≤𝟙 ()
𝟙 ω ω 𝟙 ≤ω ≤ω ()
𝟙 ω ω ≤𝟙 𝟘 𝟘 ()
𝟙 ω ω ≤𝟙 𝟘 𝟙 ()
𝟙 ω ω ≤𝟙 𝟘 ≤𝟙 ()
𝟙 ω ω ≤𝟙 𝟘 ≤ω ()
𝟙 ω ω ≤𝟙 𝟙 𝟘 ()
𝟙 ω ω ≤𝟙 𝟙 𝟙 ()
𝟙 ω ω ≤𝟙 𝟙 ≤𝟙 ()
𝟙 ω ω ≤𝟙 𝟙 ≤ω ()
𝟙 ω ω ≤𝟙 ≤𝟙 𝟘 ()
𝟙 ω ω ≤𝟙 ≤𝟙 𝟙 ()
𝟙 ω ω ≤𝟙 ≤𝟙 ≤𝟙 ()
𝟙 ω ω ≤𝟙 ≤𝟙 ≤ω ()
𝟙 ω ω ≤𝟙 ≤ω 𝟘 ()
𝟙 ω ω ≤𝟙 ≤ω 𝟙 ()
𝟙 ω ω ≤𝟙 ≤ω ≤𝟙 ()
𝟙 ω ω ≤𝟙 ≤ω ≤ω ()
𝟙 ω ω ≤ω 𝟘 𝟘 ()
𝟙 ω ω ≤ω 𝟘 𝟙 ()
𝟙 ω ω ≤ω 𝟘 ≤𝟙 ()
𝟙 ω ω ≤ω 𝟘 ≤ω ()
𝟙 ω ω ≤ω 𝟙 𝟘 ()
𝟙 ω ω ≤ω 𝟙 𝟙 ()
𝟙 ω ω ≤ω 𝟙 ≤𝟙 ()
𝟙 ω ω ≤ω 𝟙 ≤ω ()
𝟙 ω ω ≤ω ≤𝟙 𝟘 ()
𝟙 ω ω ≤ω ≤𝟙 𝟙 ()
𝟙 ω ω ≤ω ≤𝟙 ≤𝟙 ()
𝟙 ω ω ≤ω ≤𝟙 ≤ω ()
𝟙 ω ω ≤ω ≤ω 𝟘 ()
𝟙 ω ω ≤ω ≤ω 𝟙 ()
𝟙 ω ω ≤ω ≤ω ≤𝟙 ()
𝟙 ω ω ≤ω ≤ω ≤ω ()
opaque
affine⇨linear-or-affine-no-nr-reflecting :
𝟘ᵐ-allowed v₁ ≡ 𝟘ᵐ-allowed v₂ →
Is-no-nr-reflecting-morphism
(affineModality v₁)
(linear-or-affine v₂)
affine→linear-or-affine
affine⇨linear-or-affine-no-nr-reflecting {v₁ = v₁@record{}} {v₂} refl = λ where
.tr-≤-no-nr {s} → tr-≤-no-nr′ s
where
open Is-no-nr-reflecting-morphism
open Graded.Modality.Properties (affineModality v₁)
tr : Affine → Linear-or-affine
tr = affine→linear-or-affine
tr⁻¹ : Linear-or-affine → Affine
tr⁻¹ = linear-or-affine→affine
tr⁻¹-monotone : ∀ p q → p LA.≤ q → tr⁻¹ p A.≤ tr⁻¹ q
tr⁻¹-monotone = λ where
𝟘 𝟘 refl → refl
𝟙 𝟙 refl → refl
≤𝟙 𝟘 refl → refl
≤𝟙 𝟙 refl → refl
≤𝟙 ≤𝟙 refl → refl
≤ω _ _ → refl
𝟘 𝟙 ()
𝟘 ≤𝟙 ()
𝟘 ≤ω ()
𝟙 𝟘 ()
𝟙 ≤𝟙 ()
𝟙 ≤ω ()
≤𝟙 ≤ω ()
tr-tr⁻¹≤ : ∀ p → tr (tr⁻¹ p) LA.≤ p
tr-tr⁻¹≤ = λ where
𝟘 → refl
𝟙 → refl
≤𝟙 → refl
≤ω → refl
tr≤→≤tr⁻¹ : ∀ p q → tr p LA.≤ q → p A.≤ tr⁻¹ q
tr≤→≤tr⁻¹ = λ where
𝟘 𝟘 refl → refl
𝟙 𝟘 refl → refl
𝟙 𝟙 refl → refl
𝟙 ≤𝟙 refl → refl
ω _ _ → refl
𝟘 𝟙 ()
𝟘 ≤𝟙 ()
𝟘 ≤ω ()
𝟙 ≤ω ()
tr⁻¹-∧ : ∀ p q → tr⁻¹ (p LA.∧ q) ≡ tr⁻¹ p A.∧ tr⁻¹ q
tr⁻¹-∧ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
≤𝟙 𝟘 → refl
≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω → refl
≤ω _ → refl
tr⁻¹-+ : ∀ p q → tr⁻¹ (p LA.+ q) ≡ tr⁻¹ p A.+ tr⁻¹ q
tr⁻¹-+ = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
≤𝟙 𝟘 → refl
≤𝟙 𝟙 → refl
≤𝟙 ≤𝟙 → refl
≤𝟙 ≤ω → refl
≤ω 𝟘 → refl
≤ω 𝟙 → refl
≤ω ≤𝟙 → refl
≤ω ≤ω → refl
tr⁻¹-· : ∀ p q → tr⁻¹ (tr p LA.· q) ≡ p A.· tr⁻¹ q
tr⁻¹-· = λ where
𝟘 𝟘 → refl
𝟘 𝟙 → refl
𝟘 ≤𝟙 → refl
𝟘 ≤ω → refl
𝟙 𝟘 → refl
𝟙 𝟙 → refl
𝟙 ≤𝟙 → refl
𝟙 ≤ω → refl
ω 𝟘 → refl
ω 𝟙 → refl
ω ≤𝟙 → refl
ω ≤ω → refl
tr-≤-no-nr′ :
∀ s →
tr p LA.≤ q₁ →
q₁ LA.≤ q₂ →
(T (Modality-variant.𝟘ᵐ-allowed v₁) →
q₁ LA.≤ q₃) →
(⦃ 𝟘-well-behaved :
Has-well-behaved-zero Linear-or-affine
LA.linear-or-affine-semiring-with-meet ⦄ →
q₁ LA.≤ q₄) →
q₁ LA.≤ q₃ LA.+ tr r LA.· q₄ LA.+ tr s LA.· q₁ →
∃₄ λ q₁′ q₂′ q₃′ q₄′ →
tr q₂′ LA.≤ q₂ ×
tr q₃′ LA.≤ q₃ ×
tr q₄′ LA.≤ q₄ ×
p A.≤ q₁′ ×
q₁′ A.≤ q₂′ ×
(T (Modality-variant.𝟘ᵐ-allowed v₂) →
q₁′ A.≤ q₃′) ×
(⦃ 𝟘-well-behaved :
Has-well-behaved-zero Affine
(Modality.semiring-with-meet (affineModality v₂)) ⦄ →
q₁′ A.≤ q₄′) ×
q₁′ A.≤ q₃′ A.+ r A.· q₄′ A.+ s A.· q₁′
tr-≤-no-nr′ s = →tr-≤-no-nr {s = s}
(affineModality v₁)
(linear-or-affine v₂)
idᶠ
LA.linear-or-affine-has-well-behaved-zero
tr
tr⁻¹
tr⁻¹-monotone
tr≤→≤tr⁻¹
tr-tr⁻¹≤
(λ p q → ≤-reflexive (tr⁻¹-+ p q))
(λ p q → ≤-reflexive (tr⁻¹-∧ p q))
(λ p q → ≤-reflexive (tr⁻¹-· p q))